#line 1 "verify/yosupo-judge/convolution_mod_1000000007/0000.test.cpp"
/*
* @uni_kakurenbo
* https://github.com/uni-kakurenbo/competitive-programming-workspace
*
* CC0 1.0 http://creativecommons.org/publicdomain/zero/1.0/deed.ja
*/
/* #language C++ GCC */
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"
#line 2 "sneaky/enforce_int128_enable.hpp"
#ifndef __GLIBCXX_TYPE_INT_N_0
#define __GLIBCXX_BITSIZE_INT_N_0 128
#define __GLIBCXX_TYPE_INT_N_0 __int128
#endif
#line 12 "verify/yosupo-judge/convolution_mod_1000000007/0000.test.cpp"
#include <iostream>
#line 2 "snippet/aliases.hpp"
#include <cstdint>
#include <utility>
#include <vector>
#include <ranges>
#line 2 "internal/dev_env.hpp"
#ifdef LOCAL_JUDGE
inline constexpr bool DEV_ENV = true;
inline constexpr bool NO_EXCEPT = false;
#else
inline constexpr bool DEV_ENV = false;
inline constexpr bool NO_EXCEPT = true;
#endif // LOCAL_JUDGE
#if __cplusplus >= 202100L
#define CPP20 true
#define CPP23 true
#elif __cplusplus >= 202002L
#define CPP20 true
#define CPP23 false
#else
#define CPP20 false
#define CPP23 false
#endif
#line 2 "snippet/internal/types.hpp"
#line 4 "snippet/internal/types.hpp"
namespace uni {
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
#ifdef __GNUC__
using i128 = __int128_t;
using u128 = __uint128_t;
using f128 = __float128;
#endif
using uint = unsigned;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
} // namespace uni
#line 12 "snippet/aliases.hpp"
#define until(...) while(!(__VA_ARGS__))
#define CONTINUE(...) { __VA_ARGS__; continue; }
#define BREAK(...) { __VA_ARGS__; break; }
#define ALL(x) std::ranges::begin((x)),std::ranges::end((x))
#define RALL(x) std::ranges::rbegin((x)),std::ranges::rend((x))
#define $F first
#define $S second
namespace uni {
constexpr char LN = '\n';
constexpr char SPC = ' ';
constexpr std::pair<int,int> DIRS4[] = { { -1, 0 }, { 0, 1 }, { 1, 0 }, { 0, -1 } };
constexpr std::pair<int,int> DIRS4P[] = { { -1, 0 }, { 0, 1 }, { 1, 0 }, { 0, -1 }, { 0, 0 } };
constexpr std::pair<int,int> DIRS8[] = { { -1, 0 }, { -1, 1 }, { 0, 1 }, { 1, 1 }, { 1, 0 }, { 1, -1 }, { 0, -1 }, { -1, -1 } };
constexpr std::pair<int,int> DIRS8P[] = { { -1, 0 }, { -1, 1 }, { 0, 1 }, { 1, 1 }, { 1, 0 }, { 1, -1 }, { 0, -1 }, { -1, -1 }, { 0, 0 } };
template<class T> using spair = std::pair<T,T>;
} // namespace uni
namespace std {
using bit_reference = std::vector<bool>::reference;
bit_reference operator |= (bit_reference a, const bool b) noexcept(NO_EXCEPT) { return a = a | b; }
bit_reference operator &= (bit_reference a, const bool b) noexcept(NO_EXCEPT) { return a = a & b; }
}
#line 2 "snippet/fast_io.hpp"
#line 5 "snippet/fast_io.hpp"
#line 7 "snippet/fast_io.hpp"
#ifdef __GNUC__
__attribute__((constructor)) inline void fast_io() noexcept(NO_EXCEPT) { std::ios::sync_with_stdio(false), std::cin.tie(nullptr); }
#else
inline void fast_io() noexcept(NO_EXCEPT) { std::ios::sync_with_stdio(false), std::cin.tie(nullptr); }
#endif
#line 2 "adaptor/io.hpp"
#include <regex>
#line 2 "adaptor/internal/input.hpp"
#line 5 "adaptor/internal/input.hpp"
#include <string>
#line 7 "adaptor/internal/input.hpp"
#include <iterator>
#line 9 "adaptor/internal/input.hpp"
#include <tuple>
#line 11 "adaptor/internal/input.hpp"
#include <concepts>
#line 15 "adaptor/internal/input.hpp"
#line 2 "internal/resolving_rank.hpp"
namespace uni {
namespace internal {
template<int P> struct resolving_rank : resolving_rank<P-1> {};
template<> struct resolving_rank<0> {};
} // namespace internal
} // namespace uni
#line 18 "adaptor/internal/input.hpp"
#line 2 "utility/functional.hpp"
#include <functional>
#line 6 "utility/functional.hpp"
#include <type_traits>
#include <optional>
#line 2 "internal/type_traits.hpp"
#line 7 "internal/type_traits.hpp"
#include <algorithm>
#line 9 "internal/type_traits.hpp"
#line 12 "internal/type_traits.hpp"
namespace uni {
namespace internal {
template<class... Ts> struct tuple_or_pair { using type = std::tuple<Ts...>; };
template<class T, class U> struct tuple_or_pair<T,U> { using type = std::pair<T, U>; };
template <class... Ts> using tuple_or_pair_t = typename tuple_or_pair<Ts...>::type;
template<class T>
constexpr std::underlying_type_t<T> to_underlying(const T& v) noexcept(NO_EXCEPT) {
return static_cast<std::underlying_type_t<T>>(v);
}
template<class T, class... Ts>
using are_same = std::conjunction<std::is_same<T, Ts>...>;
template<class T, class... Ts>
inline constexpr bool are_same_v = are_same<T, Ts...>::value;
template<class T, class... Ts>
using is_same_as_any_of = std::disjunction<std::is_same<T, Ts>...>;
template<class T, class... Ts>
inline constexpr bool is_same_as_any_of_v = is_same_as_any_of<T, Ts...>::value;
template<class T, class... Ts>
concept same_as_any_of = is_same_as_any_of_v<T, Ts...>;
template<class Base, class... Derived>
using is_base_of_all = std::conjunction<std::is_base_of<Base, Derived>...>;
template<class Base, class... Derived>
inline constexpr bool is_base_of_all_v = is_base_of_all<Base, Derived...>::value;
template<class Base, class... Derived>
using is_base_of_any = std::disjunction<std::is_base_of<Base, Derived>...>;
template<class Base, class... Derived>
inline constexpr bool is_base_of_any_v = is_base_of_any<Base, Derived...>::value;
template<class T> struct remove_cvref {
using type = typename std::remove_cv_t<std::remove_reference_t<T>>;
};
template<class T> using remove_cvref_t = typename remove_cvref<T>::type;
template<class T> struct literal_operator { static constexpr const char* value = ""; };
template<> struct literal_operator<unsigned> { static constexpr const char* value = "U"; };
template<> struct literal_operator<long> { static constexpr const char* value = "L"; };
template<> struct literal_operator<unsigned long> { static constexpr const char* value = "UL"; };
template<> struct literal_operator<long long> { static constexpr const char* value = "LL"; };
template<> struct literal_operator<unsigned long long> { static constexpr const char* value = "ULL"; };
template<> struct literal_operator<float> { static constexpr const char* value = "F"; };
template<> struct literal_operator<double> { static constexpr const char* value = "D"; };
template<> struct literal_operator<long double> { static constexpr const char* value = "LD"; };
#ifdef __SIZEOF_INT128__
template<> struct literal_operator<__int128_t> { static constexpr const char* value = "LLL"; };
template<> struct literal_operator<__uint128_t> { static constexpr const char* value = "ULLL"; };
#endif
template<class T> inline constexpr auto literal_operator_v = literal_operator<T>::value;
template <std::size_t N, typename... Types>
struct nth_type {};
template <class Head, class... Tail>
struct nth_type<0, Head, Tail...> {
using type = Head;
};
template <std::size_t N, class Head, class... Tail>
struct nth_type<N, Head, Tail...> : public nth_type<N - 1, Tail...> {};
template <std::size_t N, typename... Types>
using nth_type_t = typename nth_type<N, Types...>::type;
template<template <class...> class, class> struct is_template_of : std::false_type {};
template<template <class...> class Template, class... Args> struct is_template_of<Template, Template<Args...>> : std::true_type {};
template<template <class...> class Template, class Type>
inline constexpr bool is_template_of_v = is_template_of<Template, Type>::value;
template<class Type, template <class...> class Template>
concept substituted_from = is_template_of_v<Template, Type>;
template<template <class...> class Base, class Derived>
struct _is_basic_tempalte_of
{
template<class... Ts>
static constexpr std::true_type test(const Base<Ts...> *);
static constexpr std::false_type test(...);
using type = decltype(test(std::declval<Derived*>()));
};
template<template <class...> class Base, class Derived>
using is_basic_tempalte_of = _is_basic_tempalte_of<Base, Derived>::type;
template<template <class...> class Base, class Derived>
inline constexpr bool is_basic_tempalte_of_v = is_basic_tempalte_of<Base, Derived>::value;
template<class Derived, template <class...> class Base>
concept derived_from_template = is_basic_tempalte_of_v<Base, Derived>;
template<class T> struct is_loggable {
template<class U>
static constexpr auto External(U &&v) -> decltype(_debug(v), std::true_type());
static constexpr std::false_type External(...);
template<class U>
static constexpr auto Member(U &&v) -> decltype(v._debug(), std::true_type());
static constexpr std::false_type Member(...);
static constexpr bool value = (
decltype(External(std::declval<T>()))::value ||
decltype(Member(std::declval<T>()))::value
);
};
template<class T>
inline constexpr auto is_loggable_v = is_loggable<T>::value;
template<class T>
concept loggable = is_loggable_v<T>;
template<class T> struct _has_iterator {
template<class U>
static constexpr auto ADL(U &&v) -> decltype(begin(v), end(v), std::true_type());
static constexpr std::false_type ADL(...);
template<class U>
static constexpr auto STL(U &&v) -> decltype(std::begin(v), std::end(v), std::true_type());
static constexpr std::false_type STL(...);
template<class U>
static constexpr auto Member(U &&v) -> decltype(v.begin(), v.end(), std::true_type());
static constexpr std::false_type Member(...);
};
template<class T> struct has_iterator {
struct ADL : decltype(_has_iterator<T>::ADL(std::declval<T>())) {};
struct STL : decltype(_has_iterator<T>::STL(std::declval<T>())) {};
struct Member : decltype(_has_iterator<T>::Member(std::declval<T>())) {};
static constexpr auto adl_v = ADL::value;
static constexpr auto stl_v = STL::value;
static constexpr auto member_v = Member::value;
};
template<class T>
struct is_iterable {
static constexpr bool value = has_iterator<T>::adl_v || has_iterator<T>::stl_v || has_iterator<T>::member_v;
};
template<class T>
inline constexpr auto is_iterable_v = is_iterable<T>::value;
template<class T>
concept iterable = is_iterable_v<T>;
namespace iterator_resolver {
template<class T>
inline constexpr auto begin(T&& v) noexcept(NO_EXCEPT) {
static_assert(is_iterable_v<T>);
if constexpr(has_iterator<T>::member_v) {
return v.begin();
}
else { // ADL
using std::begin;
return begin(std::forward<T>(v));
}
}
template<class T>
inline constexpr auto end(T&& v) noexcept(NO_EXCEPT) {
static_assert(is_iterable_v<T>);
if constexpr(has_iterator<T>::member_v) {
return v.end();
}
else { // ADL
using std::end;
return end(std::forward<T>(v));
}
}
};
template<class C> using iterator_t = decltype(iterator_resolver::begin(std::declval<C&>()));
template<class C> using container_size_t = decltype(std::size(std::declval<C&>()));
template<bool Const, class T>
using maybe_const_t = std::conditional_t<Const, const T, T>;
template<class T> using with_ref = T&;
template<class T> concept can_reference = requires { typename with_ref<T>; };
} // namespace internal
} // namespace uni
#line 11 "utility/functional.hpp"
#line 2 "utility/internal/functional_base.hpp"
namespace uni {
template<class P>
requires
requires(P p) {
p.first;
p.second;
}
inline P swapped(P& pair) {
return P{ pair.second, pair.first };
}
} // namespace uni
#line 13 "utility/functional.hpp"
#line 2 "numeric/internal/mod.hpp"
#line 2 "internal/concepts.hpp"
#line 7 "internal/concepts.hpp"
#include <limits>
#line 9 "internal/concepts.hpp"
namespace uni {
namespace internal {
template<class R, class T>
concept convertibel_range = std::convertible_to<std::ranges::range_value_t<R>, T>;
template<class T, class V>
concept item_or_convertible_range = std::convertible_to<T, V> || convertibel_range<T, V>;
template<class Structure>
concept available =
requires () {
typename Structure;
};
template<
template<class...> class Structure,
class... TemplateParameters
>
concept available_with = available<Structure<TemplateParameters...>>;
template<class T> concept arithmetic = std::is_arithmetic_v<T>;
template<class T> concept pointer = std::is_pointer_v<T>;
template<class T> concept structural = std::is_class_v<T>;
template<class Large, class Small>
concept has_double_digits_of = (std::numeric_limits<Large>::digits == 2 * std::numeric_limits<Small>::digits);
template<class Large, class Small>
concept has_more_digits_than = (std::numeric_limits<Large>::digits > std::numeric_limits<Small>::digits);
template<class Large, class Small>
concept has_or_more_digits_than = (std::numeric_limits<Large>::digits >= std::numeric_limits<Small>::digits);
template<class T>
concept has_static_zero = requires { T::zero; };
template<class T>
concept has_static_one = requires { T::one; };
template<class L, class R = L>
concept weakly_bitand_calcurable = requires (L lhs, R rhs) { lhs & rhs; };
template<class L, class R = L>
concept weakly_bitor_calcurable = requires (L lhs, R rhs) { lhs | rhs; };
template<class L, class R = L>
concept weakly_bitxor_calcurable = requires (L lhs, R rhs) { lhs ^ rhs; };
template<class L, class R = L>
concept weakly_addable = requires (L lhs, R rhs) { lhs + rhs; };
template<class L, class R = L>
concept weakly_subtractable = requires (L lhs, R rhs) { lhs - rhs; };
template<class L, class R = L>
concept weakly_multipliable = requires (L lhs, R rhs) { lhs * rhs; };
template<class L, class R = L>
concept weakly_divisable = requires (L lhs, R rhs) { lhs / rhs; };
template<class L, class R = L>
concept weakly_remainder_calculable = requires (L lhs, R rhs) { lhs % rhs; };
template<class L, class R = L>
concept weakly_bitand_assignable = requires (L lhs, R rhs) { lhs += rhs; };
template<class L, class R = L>
concept weakly_bitor_assignable = requires (L lhs, R rhs) { lhs |= rhs; };
template<class L, class R = L>
concept weakly_bitxor_assignable = requires (L lhs, R rhs) { lhs ^= rhs; };
template<class L, class R = L>
concept weakly_addition_assignable = requires (L lhs, R rhs) { lhs += rhs; };
template<class L, class R = L>
concept weakly_subtraction_assignable = requires (L lhs, R rhs) { lhs -= rhs; };
template<class L, class R = L>
concept weakly_multipliation_assignalbe = requires (L lhs, R rhs) { lhs *= rhs; };
template<class L, class R = L>
concept weakly_division_assignable = requires (L lhs, R rhs) { lhs /= rhs; };
template<class L, class R = L>
concept weakly_remainder_assignable = requires (L lhs, R rhs) { lhs /= rhs; };
template<class L, class R = L>
concept bitand_calculable =
weakly_bitand_calcurable<L, R> &&
weakly_bitand_calcurable<std::invoke_result_t<std::bit_and<>&, L, R>, R> &&
weakly_bitand_calcurable<L, std::invoke_result_t<std::bit_and<>&, L, R>> &&
weakly_bitand_calcurable<std::invoke_result_t<std::bit_and<>&, L, R>, std::invoke_result_t<std::bit_and<>&, L, R>>;
template<class L, class R = L>
concept bitor_calculable =
weakly_bitor_calcurable<L, R> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, R> &&
weakly_bitor_calcurable<L, std::invoke_result_t<std::bit_or<>&, L, R>> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, std::invoke_result_t<std::bit_or<>&, L, R>>;
template<class L, class R = L>
concept bitxor_calculable =
weakly_bitxor_calcurable<L, R> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, R> &&
weakly_bitxor_calcurable<L, std::invoke_result_t<std::bit_xor<>&, L, R>> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, std::invoke_result_t<std::bit_xor<>&, L, R>>;
template<class L, class R = L>
concept addable =
weakly_addable<L, R> &&
weakly_addable<std::invoke_result_t<std::plus<>&, L, R>, R> &&
weakly_addable<L, std::invoke_result_t<std::plus<>&, L, R>> &&
weakly_addable<std::invoke_result_t<std::plus<>&, L, R>, std::invoke_result_t<std::plus<>&, L, R>>;
template<class L, class R = L>
concept subtractable =
weakly_subtractable<L, R> &&
weakly_subtractable<std::invoke_result_t<std::minus<>&, L, R>, R> &&
weakly_subtractable<L, std::invoke_result_t<std::minus<>&, L, R>> &&
weakly_subtractable<std::invoke_result_t<std::minus<>&, L, R>, std::invoke_result_t<std::minus<>&, L, R>>;
template<class L, class R = L>
concept multipliable =
weakly_multipliable<L, R> &&
weakly_multipliable<std::invoke_result_t<std::multiplies<>&, L, R>, R> &&
weakly_multipliable<L, std::invoke_result_t<std::multiplies<>&, L, R>> &&
weakly_multipliable<std::invoke_result_t<std::multiplies<>&, L, R>, std::invoke_result_t<std::multiplies<>&, L, R>>;
template<class L, class R = L>
concept divisable =
weakly_divisable<L, R> &&
weakly_divisable<std::invoke_result_t<std::divides<>&, L, R>, R> &&
weakly_divisable<L, std::invoke_result_t<std::divides<>&, L, R>> &&
weakly_divisable<std::invoke_result_t<std::divides<>&, L, R>, std::invoke_result_t<std::divides<>&, L, R>>;
template<class L, class R = L>
concept remainder_calculable =
weakly_remainder_calculable<L, R> &&
weakly_remainder_calculable<std::invoke_result_t<std::modulus<>&, L, R>, R> &&
weakly_remainder_calculable<L, std::invoke_result_t<std::modulus<>&, L, R>> &&
weakly_remainder_calculable<std::invoke_result_t<std::modulus<>&, L, R>, std::invoke_result_t<std::modulus<>&, L, R>>;
template<class L, class R = L>
concept bitand_assignable =
weakly_bitand_assignable<L, R> &&
weakly_bitand_assignable<std::invoke_result_t<std::bit_and<>&, L, R>, R> &&
weakly_bitand_assignable<L, std::invoke_result_t<std::bit_and<>&, L, R>> &&
weakly_bitand_assignable<std::invoke_result_t<std::bit_and<>&, L, R>, std::invoke_result_t<std::bit_and<>&, L, R>>;
template<class L, class R = L>
concept bitor_assignable =
weakly_bitor_calcurable<L, R> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, R> &&
weakly_bitor_calcurable<L, std::invoke_result_t<std::bit_or<>&, L, R>> &&
weakly_bitor_calcurable<std::invoke_result_t<std::bit_or<>&, L, R>, std::invoke_result_t<std::bit_or<>&, L, R>>;
template<class L, class R = L>
concept bitxor_assignable =
weakly_bitxor_calcurable<L, R> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, R> &&
weakly_bitxor_calcurable<L, std::invoke_result_t<std::bit_xor<>&, L, R>> &&
weakly_bitxor_calcurable<std::invoke_result_t<std::bit_xor<>&, L, R>, std::invoke_result_t<std::bit_xor<>&, L, R>>;
template<class L, class R = L>
concept addition_assignable =
weakly_addition_assignable<L, R> &&
weakly_addition_assignable<std::remove_cvref_t<std::invoke_result_t<std::plus<>&, L, R>>, R> &&
weakly_addition_assignable<L, std::invoke_result_t<std::plus<>&, L, R>> &&
weakly_addition_assignable<std::remove_cvref_t<std::invoke_result_t<std::plus<>&, L, R>>, std::invoke_result_t<std::plus<>&, L, R>>;
template<class L, class R = L>
concept subtraction_assignable =
weakly_subtraction_assignable<L, R> &&
weakly_subtraction_assignable<std::remove_cvref_t<std::invoke_result_t<std::minus<>&, L, R>>, R> &&
weakly_subtraction_assignable<L, std::invoke_result_t<std::minus<>&, L, R>> &&
weakly_subtraction_assignable<std::remove_cvref_t<std::invoke_result_t<std::minus<>&, L, R>>, std::invoke_result_t<std::minus<>&, L, R>>;
template<class L, class R = L>
concept multipliation_assignalbe =
weakly_multipliation_assignalbe<L, R> &&
weakly_multipliation_assignalbe<std::remove_cvref_t<std::invoke_result_t<std::multiplies<>&, L, R>>, R> &&
weakly_multipliation_assignalbe<L, std::invoke_result_t<std::multiplies<>&, L, R>> &&
weakly_multipliation_assignalbe<std::remove_cvref_t<std::invoke_result_t<std::multiplies<>&, L, R>>, std::invoke_result_t<std::multiplies<>&, L, R>>;
template<class L, class R = L>
concept division_assignable =
weakly_division_assignable<L, R> &&
weakly_division_assignable<std::remove_cvref_t<std::invoke_result_t<std::divides<>&, L, R>>, R> &&
weakly_division_assignable<L, std::invoke_result_t<std::divides<>&, L, R>> &&
weakly_division_assignable<std::remove_cvref_t<std::invoke_result_t<std::divides<>&, L, R>>, std::invoke_result_t<std::divides<>&, L, R>>;
template<class L, class R = L>
concept remainder_assignable =
weakly_remainder_assignable<L, R> &&
weakly_remainder_assignable<std::remove_cvref_t<std::invoke_result_t<std::modulus<>&, L, R>>, R> &&
weakly_remainder_assignable<L, std::invoke_result_t<std::modulus<>&, L, R>> &&
weakly_remainder_assignable<std::remove_cvref_t<std::invoke_result_t<std::modulus<>&, L, R>>, std::invoke_result_t<std::modulus<>&, L, R>>;
template<class T>
concept weakly_incrementable =
std::movable<T> &&
requires (T v) {
{ ++v } -> std::same_as<T&>;
v++;
};
template<class T>
concept weakly_decrementable =
std::movable<T> &&
requires (T v) {
{ --v } -> std::same_as<T&>;
v--;
};
template<class T>
concept incrementable =
std::regular<T> &&
weakly_incrementable<T> &&
requires (T v) {
{ v++ } -> std::same_as<T>;
};
template<class T>
concept decrementable =
std::regular<T> &&
weakly_decrementable<T> &&
requires (T v) {
{ v-- } -> std::same_as<T>;
};
template<class L, class R = L>
concept weakly_arithmetic_operable =
weakly_addable<L, R> &&
weakly_subtractable<L, R> &&
weakly_multipliable<L, R> &&
weakly_divisable<L, R>;
template<class L, class R = L>
concept weakly_arithmetic_operation_assignable =
weakly_addition_assignable<L, R> &&
weakly_subtraction_assignable<L, R> &&
weakly_multipliation_assignalbe<L, R> &&
weakly_division_assignable<L, R>;
template<class L, class R = L>
concept arithmetic_operable =
weakly_arithmetic_operable<L, R> &&
addable<L, R> &&
subtractable<L, R> &&
multipliable<L, R> &&
divisable<L, R>;
template<class L, class R = L>
concept arithmetic_operation_assignable =
weakly_arithmetic_operation_assignable<L, R> &&
addition_assignable<L, R> &&
subtraction_assignable<L, R> &&
multipliation_assignalbe<L, R> &&
division_assignable<L, R>;
template<class T>
concept unary_addable =
requires (T v) {
{ +v } -> std::same_as<T>;
};
template<class T>
concept unary_subtractable =
requires (T v) {
{ -v } -> std::same_as<T>;
};
template<class T>
concept numeric =
std::regular<T> &&
arithmetic_operable<T> &&
arithmetic_operation_assignable<T> &&
weakly_incrementable<T> &&
unary_addable<T> &&
unary_subtractable<T>;
} // namespace internal
} // namespace uni
#line 6 "numeric/internal/mod.hpp"
namespace uni {
template<class T, class R>
requires
internal::remainder_calculable<T, R> &&
internal::subtractable<T, R> &&
internal::unary_subtractable<T>
inline T mod(T x, const R& r) noexcept(NO_EXCEPT) {
if(x >= 0) return x % r;
x = -x % r;
if(x != 0) x = r - x;
return x;
}
} // namespace uni
#line 2 "numeric/arithmetic.hpp"
#include <cassert>
#include <cstring>
#line 13 "numeric/arithmetic.hpp"
#include <bit>
#include <atcoder/math>
#line 2 "snippet/iterations.hpp"
#line 2 "macro/overload.hpp"
#define $OVERLOAD2(arg0, arg1, cmd, ...) cmd
#define $OVERLOAD3(arg0, arg1, arg2, cmd, ...) cmd
#define $OVERLOAD4(arg0, arg1, arg2, arg3, cmd, ...) cmd
#define $OVERLOAD5(arg0, arg1, arg2, arg3, arg4, cmd, ...) cmd
#define $OVERLOAD6(arg0, arg1, arg2, arg3, arg4, arg5, cmd, ...) cmd
#line 2 "macro/basic.hpp"
#define TO_STRING_AUX(x) #x
#define TO_STRING(x) TO_STRING_AUX(x)
#define CONCAT_AUX(x, y) x##y
#define CONCAT(x, y) CONCAT_AUX(x, y)
#define UNPAREN_AUX(...) __VA_ARGS__
#define UNPAREN(...) __VA_ARGS__
#line 6 "snippet/iterations.hpp"
#define LOOP(n) REPI(CONCAT(_$, __COUNTER__), n)
#define REPI(i,n) for(std::remove_cvref_t<decltype(n)> i=0, CONCAT(i, $)=(n); i<CONCAT(i, $); ++i)
#define REPF(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(l), CONCAT(i, $)=(r); i<CONCAT(i, $); ++i)
#define REPIS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l), CONCAT(i, $)=(r); i<CONCAT(i, $); i+=(s))
#define REPR(i,n) for(auto i=(n); --i>=0;)
#define REPB(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(r), CONCAT(i, $)=(l); --i>=CONCAT(i, $);)
#define REPRS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l)+((r)-(l)-1)/(s)*(s), CONCAT(i, $)=(l); i>=CONCAT(i, $); (i-=(s)))
#define REP(...) $OVERLOAD4(__VA_ARGS__, REPIS, REPF, REPI, LOOP)(__VA_ARGS__)
#define REPD(...) $OVERLOAD4(__VA_ARGS__, REPRS, REPB, REPR)(__VA_ARGS__)
#define FORO(i,n) for(int i=0, CONCAT(i, $)=static_cast<int>(n); i<=CONCAT(i, $); ++i)
#define FORI(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(l), CONCAT(i, $)=(r); i<=CONCAT(i, $); ++i)
#define FORIS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l), CONCAT(i, $)=(r); i<=CONCAT(i, $); i+=(s))
#define FORRO(i,n) for(auto i=(n); i>=0; --i)
#define FORR(i,l,r) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>> i=(r), CONCAT(i, $)=(l); i>=CONCAT(i, $); --i)
#define FORRS(i,l,r,s) for(std::common_type_t<std::remove_cvref_t<decltype(l)>,std::remove_cvref_t<decltype(r)>,std::remove_cvref_t<decltype(s)>> i=(l)+((r)-(l))/(s)*(s), CONCAT(i, $)=(l); i>=CONCAT(i, $); i-=(s))
#define FOR(...) $OVERLOAD4(__VA_ARGS__, FORIS, FORI, FORO)(__VA_ARGS__)
#define FORD(...) $OVERLOAD4(__VA_ARGS__, FORRS, FORR, FORRO)(__VA_ARGS__)
#define ITR1(e0,v) for(const auto &e0 : (v))
#define ITRP1(e0,v) for(auto e0 : (v))
#define ITRR1(e0,v) for(auto &e0 : (v))
#define ITR2(e0,e1,v) for(const auto [e0, e1] : (v))
#define ITRP2(e0,e1,v) for(auto [e0, e1] : (v))
#define ITRR2(e0,e1,v) for(auto &[e0, e1] : (v))
#define ITR3(e0,e1,e2,v) for(const auto [e0, e1, e2] : (v))
#define ITRP3(e0,e1,e2,v) for(auto [e0, e1, e2] : (v))
#define ITRR3(e0,e1,e2,v) for(auto &[e0, e1, e2] : (v))
#define ITR4(e0,e1,e2,e3,v) for(const auto [e0, e1, e2, e3] : (v))
#define ITRP4(e0,e1,e2,e3,v) for(auto [e0, e1, e2, e3] : (v))
#define ITRR4(e0,e1,e2,e3,v) for(auto &[e0, e1, e2, e3] : (v))
#define ITR5(e0,e1,e2,e3,e4,v) for(const auto [e0, e1, e2, e3, e4] : (v))
#define ITRP5(e0,e1,e2,e3,e4,v) for(auto [e0, e1, e2, e3, e4] : (v))
#define ITRR5(e0,e1,e2,e3,e4,v) for(auto &[e0, e1, e2, e3, e4] : (v))
#define ITR(...) $OVERLOAD6(__VA_ARGS__, ITR5, ITR4, ITR3, ITR2, ITR1)(__VA_ARGS__)
#define ITRP(...) $OVERLOAD6(__VA_ARGS__, ITRP5, ITRP4, ITRP3, ITRP2, ITRP1)(__VA_ARGS__)
#define ITRR(...) $OVERLOAD6(__VA_ARGS__, ITRR5, ITRR4, ITRR3, ITRR2, ITRR1)(__VA_ARGS__)
#line 21 "numeric/arithmetic.hpp"
#line 2 "internal/types.hpp"
#line 4 "internal/types.hpp"
namespace uni {
namespace internal {
using size_t = std::int64_t;
using int128_t = __int128_t;
using uint128_t = __uint128_t;
} // namesapce internal
} // namespace uni
#line 25 "numeric/arithmetic.hpp"
#line 27 "numeric/arithmetic.hpp"
#line 2 "numeric/internal/number_base.hpp"
#line 5 "numeric/internal/number_base.hpp"
#include <cstddef>
#include <string_view>
#line 14 "numeric/internal/number_base.hpp"
#line 18 "numeric/internal/number_base.hpp"
#line 2 "adaptor/string.hpp"
#line 6 "adaptor/string.hpp"
#line 2 "adaptor/internal/advanced_container.hpp"
#line 8 "adaptor/internal/advanced_container.hpp"
#line 11 "adaptor/internal/advanced_container.hpp"
#line 15 "adaptor/internal/advanced_container.hpp"
#line 2 "iterable/internal/operation_base.hpp"
#line 6 "iterable/internal/operation_base.hpp"
#include <sstream>
#include <numeric>
#line 11 "iterable/internal/operation_base.hpp"
namespace uni {
template<std::input_iterator I, std::sentinel_for<I> S>
std::string join(I first, S last, const char* sep = "") noexcept(NO_EXCEPT) {
if(first == last) return "";
std::ostringstream res;
while(true) {
res << *first;
std::ranges::advance(first, 1);
if(first == last) break;
res << sep;
}
return res.str();
}
template<std::ranges::input_range R>
std::string join(R&& range, const char* sep = "") noexcept(NO_EXCEPT) {
return join(ALL(range), sep);
}
template<class I, class T = std::iter_value_t<I>>
requires std::sentinel_for<I, I>
T sum(I first, I last, const T& base = T()) noexcept(NO_EXCEPT) {
return std::accumulate(first, last, base);
}
template<std::ranges::input_range R, class T = std::ranges::range_value_t<R>>
auto sum(R&& range, T base = T()) noexcept(NO_EXCEPT) {
auto&& r = range | std::views::common;
return sum(ALL(r), base);
}
} // namesapce uni
#line 18 "adaptor/internal/advanced_container.hpp"
#define UNI_ADVANCED_CONTAINER_OPERATOR(op_assign, op, concepts) \
auto& operator op_assign(const value_type& v) noexcept(NO_EXCEPT) \
requires concepts<value_type> \
{ \
if constexpr(concepts<Base, value_type>) { \
this->Base::operator op_assign(v); \
} \
else { \
REP(itr, ALL(*this)) *itr op_assign v; \
} \
return *this; \
} \
\
auto& operator op_assign(const advanced_container& rhs) noexcept(NO_EXCEPT) \
requires concepts<value_type> \
{ \
if constexpr(concepts<Base>) { \
this->Base::operator op_assign(*rhs._base()); \
} \
else { \
auto itr = std::ranges::begin(*this), rhs_itr = std::ranges::begin(rhs); \
auto end = std::ranges::end(*this); \
for(; itr != end; ++itr, ++rhs_itr) { \
*itr op_assign *rhs_itr; \
} \
} \
return *this; \
} \
\
template<class T = value_type> \
requires \
concepts<value_type> && \
(std::convertible_to<T, value_type> || std::same_as<T, advanced_container>) \
friend auto operator op(advanced_container lhs, const T& rhs) noexcept(NO_EXCEPT) { \
return lhs op_assign rhs; \
} \
\
template<class T = value_type> \
requires \
concepts<value_type> && std::convertible_to<T, value_type> \
friend auto operator op(const T& lhs, advanced_container rhs) noexcept(NO_EXCEPT) { \
return advanced_container(rhs.size(), lhs) op_assign rhs; \
}
namespace uni {
namespace internal {
template<class Base>
struct advanced_container : Base {
private:
inline Base* _base() noexcept(NO_EXCEPT) {
return static_cast<Base*>(this);
}
inline const Base* _base() const noexcept(NO_EXCEPT) {
return static_cast<const Base*>(this);
}
public:
using Base::Base;
advanced_container(const Base& base) : Base(base) {}
using size_type = decltype(std::ranges::size(std::declval<Base>()));
using value_type = Base::value_type;
inline auto ssize() const noexcept(NO_EXCEPT) { return std::ranges::ssize(*this->_base()); }
inline const auto& operator[](internal::size_t p) const noexcept(NO_EXCEPT) {
p = p < 0 ? p + this->size() : p;
assert(0 <= p && p < this->ssize());
return this->Base::operator[](p);
}
inline auto& operator[](internal::size_t p) noexcept(NO_EXCEPT) {
p = p < 0 ? p + this->size() : p;
assert(0 <= p && p < this->ssize());
return this->Base::operator[](p);
}
inline auto& fill(const value_type& v) noexcept(NO_EXCEPT) {
std::ranges::fill(*this, v);
return *this;
}
inline auto& swap(const size_type i, const size_type j) noexcept(NO_EXCEPT) {
std::swap(this->operator[](i), this->operator[](j));
return *this;
}
inline auto& sort() noexcept(NO_EXCEPT) {
std::ranges::sort(*this);
return *this;
}
template<class F>
inline auto& sort(F&& f) noexcept(NO_EXCEPT) {
std::ranges::sort(*this, std::forward<F>(f));
return *this;
}
inline auto& stable_sort() noexcept(NO_EXCEPT) {
std::ranges::stable_sort(*this);
return *this;
}
template<class F>
inline auto& stable_sort(F&& f) noexcept(NO_EXCEPT) {
std::ranges::stable_sort(*this, std::forward<F>(f));
return *this;
}
inline auto& reverse() noexcept(NO_EXCEPT) {
std::ranges::reverse(*this);
return *this;
}
inline auto count(const value_type& v) const noexcept(NO_EXCEPT) {
return std::ranges::count(*this, v);
}
template<class F>
inline auto count_if(F&& f) const noexcept(NO_EXCEPT) {
return std::ranges::count_if(*this, std::forward<F>(f));
}
inline auto& resize(const size_type k) noexcept(NO_EXCEPT) {
this->Base::resize(k);
return *this;
}
inline auto& resize(const size_type k, const value_type v) noexcept(NO_EXCEPT) {
this->Base::resize(k, v);
return *this;
}
template<class F>
inline auto& shuffle(F&& f) noexcept(NO_EXCEPT) {
std::ranges::shuffle(*this, std::forward<F>(f));
return *this;
}
inline auto& unique() noexcept(NO_EXCEPT) {
const auto rest = std::ranges::unique(*this);
this->erase(ALL(rest));
return *this;
}
template<class T>
inline auto binary_search(const T& v) noexcept(NO_EXCEPT) {
return std::ranges::binary_search(*this, v);
}
template<class T>
inline auto lower_bound(const T& v) noexcept(NO_EXCEPT) {
return std::ranges::lower_bound(*this, v);
}
template<class T>
inline auto upper_bound(const T& v) noexcept(NO_EXCEPT) {
return std::ranges::upper_bound(*this, v);
}
inline auto join(const char* sep = "") noexcept(NO_EXCEPT) {
return uni::join(*this, sep);
}
inline auto sum() const noexcept(NO_EXCEPT) { return uni::sum(*this); }
inline auto max() const noexcept(NO_EXCEPT) { return std::ranges::max(*this->_base()); }
inline auto min() const noexcept(NO_EXCEPT) { return std::ranges::min(*this); }
inline auto begin() noexcept(NO_EXCEPT) { return std::ranges::begin(*this->_base()); }
inline auto begin() const noexcept(NO_EXCEPT) { return std::ranges::begin(*this->_base()); }
inline auto end() noexcept(NO_EXCEPT) { return std::ranges::end(*this->_base()); }
inline auto end() const noexcept(NO_EXCEPT) { return std::ranges::end(*this->_base()); }
UNI_ADVANCED_CONTAINER_OPERATOR(+=, +, internal::weakly_addition_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(-=, -, internal::weakly_subtraction_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(*=, *, internal::weakly_multipliation_assignalbe)
UNI_ADVANCED_CONTAINER_OPERATOR(/=, /, internal::weakly_division_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(%=, %, internal::weakly_remainder_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(&=, &, internal::weakly_bitand_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(|=, |, internal::weakly_bitor_assignable)
UNI_ADVANCED_CONTAINER_OPERATOR(^=, ^, internal::weakly_bitxor_assignable)
};
} // namespace internal
} // namespace uni
#undef UNI_ADVANCED_CONTAINER_OPERATOR
#line 8 "adaptor/string.hpp"
namespace uni {
using string = internal::advanced_container<std::string>;
} // namespace uni
namespace std {
template<>
struct hash<uni::string> {
inline auto operator()(const uni::string& key) const noexcept(NO_EXCEPT) {
return std::hash<std::string>{}(static_cast<std::string>(key));
}
};
}
#line 2 "adaptor/vector.hpp"
#line 6 "adaptor/vector.hpp"
#line 9 "adaptor/vector.hpp"
namespace uni {
template<class... Args>
using vector = internal::advanced_container<std::vector<Args...>>;
} // namespace uni
#line 21 "numeric/internal/number_base.hpp"
namespace uni {
template<std::size_t B, class T>
uni::string to_base_n_string(T v) noexcept(NO_EXCEPT) {
constexpr std::string_view CHARS = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
static_assert(0 < B and B <= std::ranges::size(CHARS));
assert(0 <= v);
uni::string res;
while(v > 0) {
res += CHARS[v%B];
v /= B;
}
std::reverse(ALL(res));
return res;
}
template<class T>
uni::string to_base_n_string(T v, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
constexpr std::string_view CHARS = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
assert(1 < b && b <= std::ranges::ssize(CHARS));
assert(0 <= v);
if(v == 0) return "0";
uni::string res;
while(v > 0) {
res += CHARS[v % b];
v /= b;
}
std::reverse(ALL(res));
return res;
}
template<class T>
uni::vector<T> to_base_n_vector(T v, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
assert(1 < b);
assert(0 <= v);
uni::vector<T> res;
while(v > 0) {
res.push_back(v%b);
v /= b;
}
return res;
}
template<std::bidirectional_iterator I, class T = typename std::iterator_traits<I>::value_type>
T from_base_n_sequence(I begin, I end, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
assert(1 < b);
if(begin == end) return 0;
T res = 0;
for(auto itr=end; itr-- != begin; ) {
res *= b;
res += *itr;
}
return res;
}
template<class T, std::forward_iterator I>
T from_base_n_string(I begin, I end, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
assert(1 < b);
if(begin == end) return 0;
T sgn = 1;
if(*begin == '-') {
sgn = -1;
++begin;
}
T res = 0;
for(auto itr=begin; itr != end; ++itr) {
res *= b;
if('0' <= *itr && *itr <= '9') {
res += *itr - '0';
}
else if('a' <= *itr && *itr <= 'z') {
res += *itr - 'a' + 10;
}
else if('A' <= *itr && *itr <= 'Z'){
res += *itr - 'A' + 10;
}
else {
assert(false);
}
}
return res * sgn;
}
template<std::ranges::bidirectional_range R, class T = std::ranges::range_value_t<R>>
requires std::ranges::common_range<R>
T from_base_n_sequence(R range, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
return from_base_n_sequence(std::ranges::begin(range), std::ranges::end(range), b);
}
template<class T, std::ranges::bidirectional_range R>
requires std::ranges::common_range<R>
T from_base_n_string(R range, const uni::internal::size_t b) noexcept(NO_EXCEPT) {
return from_base_n_string<T>(std::ranges::begin(range), std::ranges::end(range), b);
}
} // namespace uni
#line 29 "numeric/arithmetic.hpp"
#line 2 "iterable/operation.hpp"
#line 6 "iterable/operation.hpp"
#include <initializer_list>
#line 9 "iterable/operation.hpp"
#include <valarray>
#line 17 "iterable/operation.hpp"
#line 21 "iterable/operation.hpp"
#line 2 "internal/exception.hpp"
namespace uni {
namespace internal {
template<class... T> inline constexpr bool EXCEPTION_ON_TYPE = false;
template<auto T> inline constexpr bool EXCEPTION_ON_VALUE = false;
} // namespace internal
} // namespace uni
#line 2 "internal/iterator.hpp"
#line 7 "internal/iterator.hpp"
#include <variant>
#include <compare>
#line 10 "internal/iterator.hpp"
#line 13 "internal/iterator.hpp"
#line 16 "internal/iterator.hpp"
namespace uni {
namespace internal {
template<class T>
struct iterator_interface {
using iterator_category = std::output_iterator_tag;
using difference_type = size_t;
using value_type = T;
using pointer = T*;
using reference = T&;
// virtual T operator*() const noexcept(NO_EXCEPT) { return 0; };
};
template<class T>
struct forward_iterator : iterator_interface<T> {
using iterator_category = std::forward_iterator_tag;
// virtual bidirectional_iterator_interface& operator++() = 0;
};
template<class T>
struct bidirectional_iterator_interface : forward_iterator<T> {
using iterator_category = std::bidirectional_iterator_tag;
// virtual bidirectional_iterator_interface& operator--() = 0;
};
template<class T>
struct random_access_iterator_base : bidirectional_iterator_interface<T> {
using iterator_category = std::random_access_iterator_tag;
using difference_type = typename bidirectional_iterator_interface<T>::difference_type;
public:
// virtual random_access_iterator_base& operator+=(const difference_type count) = 0;
// virtual random_access_iterator_base& operator-=(const difference_type count) = 0;
friend inline random_access_iterator_base operator+(random_access_iterator_base itr, const difference_type count) noexcept(NO_EXCEPT) { return itr += count, itr; }
friend inline random_access_iterator_base operator-(random_access_iterator_base itr, const difference_type count) noexcept(NO_EXCEPT) { return itr -= count, itr; }
};
template<class T, class Container, class Derived>
struct container_iterator_interface : random_access_iterator_base<T> {
using difference_type = std::make_signed_t<typename Container::size_type>;
private:
using derived = std::remove_cvref_t<Derived>;
Container* _ref;
difference_type _pos;
static_assert(std::three_way_comparable<difference_type>);
inline auto* _derived() noexcept(NO_EXCEPT) {
return static_cast<derived*>(this);
}
inline const auto* _derived() const noexcept(NO_EXCEPT) {
return static_cast<const derived*>(this);
}
public:
container_iterator_interface() noexcept = default;
container_iterator_interface(Container *const ref, const difference_type pos) noexcept(NO_EXCEPT) : _ref(ref), _pos(pos) {}
inline auto ref() const noexcept(NO_EXCEPT) { return this->_ref; }
inline auto pos() const noexcept(NO_EXCEPT) { return this->_pos; }
inline auto& pos() { return this->_pos; }
inline auto& operator++() noexcept(NO_EXCEPT) { return ++this->_pos, *this->_derived(); }
inline auto& operator--() noexcept(NO_EXCEPT) { return --this->_pos, *this->_derived(); }
inline auto operator++(int) noexcept(NO_EXCEPT) { auto res = *this->_derived(); return ++this->_pos, res; }
inline auto operator--(int) noexcept(NO_EXCEPT) { auto res = *this->_derived(); return --this->_pos, res; }
inline auto& operator+=(const difference_type count) noexcept(NO_EXCEPT) { return this->_pos += count, *this->_derived(); }
inline auto& operator-=(const difference_type count) noexcept(NO_EXCEPT) { return this->_pos -= count, *this->_derived(); }
inline auto operator*() const noexcept(NO_EXCEPT) { return this->ref()->get(this->_pos); }
inline auto operator[](const difference_type count) const noexcept(NO_EXCEPT) { return *(*this->_derived() + count); }
inline auto operator-(const derived& other) const noexcept(NO_EXCEPT) { return this->_pos - other._pos; }
friend inline bool operator==(const derived& lhs, const derived& rhs) noexcept(NO_EXCEPT) {
if(lhs.ref() == rhs.ref()) return lhs._pos == rhs._pos;
return false;
}
friend inline std::partial_ordering operator<=>(const derived& lhs, const derived& rhs) noexcept(NO_EXCEPT) {
if(lhs.ref() != rhs.ref()) return std::partial_ordering::unordered;
return lhs._pos <=> rhs._pos;
}
};
namespace iterator_impl {
template<class... Tags>
using is_all_random_access_iterator = is_base_of_all<std::random_access_iterator_tag,Tags...>;
template<class... Tags>
using is_all_bidirectional_iterator = is_base_of_all<std::bidirectional_iterator_tag,Tags...>;
template<class... Tags>
using is_all_forward_iterator = is_base_of_all<std::forward_iterator_tag,Tags...>;
template<class... Tags>
using is_all_input_iterator = is_base_of_all<std::input_iterator_tag,Tags...>;
template<class... Tags>
constexpr auto _most_primitive_iterator_tag() {
if constexpr(is_all_random_access_iterator<Tags...>::value) {
return std::random_access_iterator_tag{};
}
else if constexpr(is_all_bidirectional_iterator<Tags...>::value) {
return std::bidirectional_iterator_tag{};
}
else if constexpr(is_all_forward_iterator<Tags...>::value) {
return std::forward_iterator_tag{};
}
else {
return std::input_iterator_tag{};
}
}
} // namespace iterator_impl
template<class... Tags>
using most_primitive_iterator_tag = decltype(iterator_impl::_most_primitive_iterator_tag<Tags...>());
template<class T, class = void>
struct is_iterator {
static constexpr bool value = false;
};
template<class T>
struct is_iterator<T, typename std::enable_if<!std::is_same<typename std::iterator_traits<T>::value_type, void>::value>::type> {
static constexpr bool value = true;
};
template<class T>
inline constexpr bool is_iterator_v = is_iterator<T>::value;
template<class T>
using is_iterator_t = std::enable_if_t<is_iterator_v<T>>;
template<class T>
using iota_diff_t = std::make_signed_t<T>;
} // namespace internal
} // namespace uni
#line 2 "internal/ranges.hpp"
#line 7 "internal/ranges.hpp"
#line 11 "internal/ranges.hpp"
namespace uni {
namespace internal {
template<class Range>
concept resizable_range
= std::ranges::range<Range> &&
requires (Range& r) { r.resize(0); };
template<class range>
concept simple_view
= std::ranges::view<range> && std::ranges::range<const range> &&
std::same_as<std::ranges::iterator_t<range>, std::ranges::iterator_t<const range>> &&
std::same_as<std::ranges::sentinel_t<range>, std::ranges::sentinel_t<const range>>;
template<class... Ranges>
concept zip_is_common = (sizeof...(Ranges) == 1 && (std::ranges::common_range<Ranges> && ...))
|| (!(std::ranges::bidirectional_range<Ranges> && ...) && (std::ranges::common_range<Ranges> && ...))
|| ((std::ranges::random_access_range<Ranges> && ...) && (std::ranges::sized_range<Ranges> && ...));
template<bool Const, class... Views>
concept all_contiguous = (std::ranges::contiguous_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views>
concept all_random_access = (std::ranges::random_access_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views>
concept all_bidirectional = (std::ranges::bidirectional_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views>
concept all_forward = (std::ranges::forward_range<maybe_const_t<Const, Views>> && ...);
template<bool Const, class... Views> struct zip_view_iterator_category {};
template<bool Const, class... Views>
requires all_forward<Const, Views...>
struct zip_view_iterator_category<Const, Views...> {
using iterator_category = std::input_iterator_tag;
};
template<bool Const, class... Views>
static auto _most_primitive_iterator_concept() noexcept(NO_EXCEPT) {
if constexpr(all_random_access<Const, Views...>)
return std::random_access_iterator_tag{};
else if constexpr(all_bidirectional<Const, Views...>)
return std::bidirectional_iterator_tag{};
else if constexpr(all_forward<Const, Views...>)
return std::forward_iterator_tag{};
else
return std::input_iterator_tag{};
}
template<bool Const, class... Views>
using most_primitive_iterator_concept = decltype(_most_primitive_iterator_concept<Const, Views...>());
template<class Range, bool Const>
using range_iterator_category = typename std::iterator_traits<
std::ranges::iterator_t<maybe_const_t<Const, Range>>
>::iterator_category;
template<class Range>
static constexpr auto _iterator_concept() noexcept(NO_EXCEPT) {
if constexpr(std::ranges::random_access_range<Range>)
return std::random_access_iterator_tag{};
else if constexpr(std::ranges::bidirectional_range<Range>)
return std::bidirectional_iterator_tag{};
else if constexpr(std::ranges::forward_range<Range>)
return std::forward_iterator_tag{};
else
return std::input_iterator_tag{};
}
template<class Range>
using iterator_concept = decltype(_iterator_concept<Range>());
template<std::ranges::range Range> struct cached_position {
constexpr bool has_value() const { return false; }
constexpr std::ranges::iterator_t<Range> get(const Range&) const {
__builtin_unreachable();
}
constexpr void set(const Range &, const std::ranges::iterator_t<Range> &) const {}
};
template<std::ranges::forward_range Range>
struct cached_position<Range> : protected std::optional<std::ranges::iterator_t<Range>> {
using std::optional<std::ranges::iterator_t<Range>>::optioanl;
using std::optional<std::ranges::iterator_t<Range>>::has_value;
constexpr std::ranges::iterator_t<Range> get(const Range&) const {
assert(this->has_value());
return **this;
}
constexpr void set(const Range&, const std::ranges::iterator_t<Range>& itr) {
assert(!this->has_value());
this->emplace(*itr);
}
};
template<std::ranges::random_access_range Range>
requires(sizeof(std::ranges::range_difference_t<Range>) <= sizeof(std::ranges::iterator_t<Range>))
struct cached_position<Range> {
private:
std::ranges::range_difference_t<Range> _offset = -1;
public:
cached_position() = default;
constexpr cached_position(const cached_position &) = default;
constexpr cached_position(cached_position &&other) noexcept {
*this = std::move(other);
}
constexpr cached_position &operator=(const cached_position &) = default;
constexpr cached_position &operator=(cached_position &&other) noexcept {
// Propagate the cached offset, but invalidate the source.
this->_offset = other._offset;
other._offset = -1;
return *this;
}
constexpr bool has_value() const { return this->_offset >= 0; }
constexpr std::ranges::iterator_t<Range> get(Range& range) const {
assert(this->has_value());
return std::ranges::begin(range) + this->_offset;
}
constexpr void set(Range &range, const std::ranges::iterator_t<Range> &itr) {
assert(!this->has_value());
this->_offset = itr - std::ranges::begin(range);
}
};
template<typename T, int Disc>
struct absent { };
template<bool PRESENT, class T, int Disc = 0>
using maybe_present_t = std::conditional_t<PRESENT, T, absent<T, Disc>>;
} // namespace internal
namespace views::adaptor {
template<class Adaptor, class... Args>
concept adaptor_invocable = requires { std::declval<Adaptor>()(std::declval<Args>()...); };
template<class Adaptor, class... Args>
concept adaptor_partial_app_viable =
(Adaptor::arity > 1) && (sizeof...(Args) == Adaptor::arity - 1) &&
(std::constructible_from<std::remove_cvref_t<Args>, Args> && ...);
template<class Adaptor, class... Args> struct partial;
template<class, class> struct pipe;
template<class Derived> struct range_adaptor_closure {};
template<class T, class U>
requires(!std::same_as<T, range_adaptor_closure<U>>)
void is_range_adaptor_closure_fn(const T &, const range_adaptor_closure<U> &);
template<class T>
concept is_range_adaptor_closure = requires(T t) { adaptor::is_range_adaptor_closure_fn(t, t); };
template<class Self, class Range>
requires is_range_adaptor_closure<Self> && adaptor_invocable<Self, Range>
constexpr auto operator|(Range&& range, Self&& self) {
return std::forward<Self>(self)(std::forward<Range>(range));
}
template<class Lhs, class Rhs>
requires is_range_adaptor_closure<Lhs> && is_range_adaptor_closure<Rhs>
constexpr auto operator|(Lhs&& lhs, Rhs&& rhs) {
return pipe<std::remove_cvref_t<Lhs>, std::remove_cvref_t<Rhs>>{ std::forward<Lhs>(lhs), std::forward<Rhs>(rhs)};
}
template<class Derived> struct range_adaptor {
template<class... Args>
requires adaptor_partial_app_viable<Derived, Args...>
inline constexpr auto operator()(Args&& ..._args) const noexcept(NO_EXCEPT) {
return partial<Derived, std::remove_cvref_t<Args>...>{
std::forward<Args>(_args)...
};
}
};
template<class Adaptor>
concept closure_has_simple_call_op = Adaptor::has_simple_call_op;
template<class Adaptor, class... Args>
concept adaptor_has_simple_extra_args =
Adaptor::has_simple_extra_args ||
Adaptor::template has_simple_extra_args<Args...>;
template<class Adaptor, class... Args>
struct partial : range_adaptor_closure<partial<Adaptor, Args...>> {
std::tuple<Args...> args;
constexpr partial(Args... _args) noexcept(NO_EXCEPT) : args(std::move(_args)...) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Args &...>
inline constexpr auto operator()(Range&& range) const & noexcept(NO_EXCEPT) {
const auto forwarder = [&range](const auto &..._args) constexpr noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), _args...);
};
return std::apply(forwarder, this->args);
}
template<class Range>
requires adaptor_invocable<Adaptor, Range, Args...>
inline constexpr auto operator()(Range&& range) && noexcept(NO_EXCEPT) {
const auto forwarder = [&range](auto &..._args) constexpr noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), std::move(_args)...);
};
return std::apply(forwarder, this->args);
}
template<class Range>
inline constexpr auto operator()(Range&& range) const && = delete;
};
template<class Adaptor, class Arg>
struct partial<Adaptor, Arg> : range_adaptor_closure<partial<Adaptor, Arg>> {
Arg arg;
constexpr partial(Arg _arg) noexcept(NO_EXCEPT) : arg(std::move(_arg)) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Arg &>
inline constexpr auto operator()(Range&& range) const & noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), this->arg);
}
template<class Range>
requires adaptor_invocable<Adaptor, Range, Arg>
inline constexpr auto operator()(Range&& range) && noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), std::move(this->arg));
}
template<class Range>
inline constexpr auto operator()(Range&& range) const && = delete;
};
template<class Adaptor, class... Args>
requires adaptor_has_simple_extra_args<Adaptor, Args...> && (std::is_trivially_copyable_v<Args> && ...)
struct partial<Adaptor, Args...> : range_adaptor_closure<partial<Adaptor, Args...>> {
std::tuple<Args...> args;
constexpr partial(Args... _args) noexcept(NO_EXCEPT) : args(std::move(_args)...) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Args &...>
inline constexpr auto operator()(Range&& range) const noexcept(NO_EXCEPT) {
const auto forwarder = [&range](const auto &..._args) constexpr noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), _args...);
};
return std::apply(forwarder, this->args);
}
static constexpr bool has_simple_call_op = true;
};
template<class Adaptor, class Arg>
requires adaptor_has_simple_extra_args<Adaptor, Arg> &&
std::is_trivially_copyable_v<Arg>
struct partial<Adaptor, Arg> : range_adaptor_closure<partial<Adaptor, Arg>> {
Arg arg;
constexpr partial(Arg _arg) noexcept(NO_EXCEPT) : arg(std::move(_arg)) {}
template<class Range>
requires adaptor_invocable<Adaptor, Range, const Arg &>
inline constexpr auto operator()(Range&& range) const noexcept(NO_EXCEPT) {
return Adaptor{}(std::forward<Range>(range), this->arg);
}
static constexpr bool has_simple_call_op = true;
};
template<class Lhs, class Rhs, class Range>
concept pipe_invocable = requires {
std::declval<Rhs>()(std::declval<Lhs>()(std::declval<Range>()));
};
template<class Lhs, class Rhs> struct pipe : range_adaptor_closure<pipe<Lhs, Rhs>> {
[[no_unique_address]] Lhs lhs;
[[no_unique_address]] Rhs rhs;
constexpr pipe(Lhs _lhs, Rhs _rhs) noexcept(NO_EXCEPT) : lhs(std::move(_lhs)), rhs(std::move(_rhs)) {}
template<class Range>
requires pipe_invocable<const Lhs &, const Rhs &, Range>
inline constexpr auto operator()(Range&& range) const & noexcept(NO_EXCEPT) {
return rhs(lhs(std::forward<Range>(range)));
}
template<class Range>
requires pipe_invocable<Lhs, Rhs, Range>
inline constexpr auto operator()(Range&& range) && noexcept(NO_EXCEPT) {
return std::move(rhs)(std::move(lhs)(std::forward<Range>(range)));
}
template<class Range>
inline constexpr auto operator()(Range&& range) const && = delete;
};
template<class Lhs, class Rhs>
requires closure_has_simple_call_op<Lhs> && closure_has_simple_call_op<Rhs>
struct pipe<Lhs, Rhs> : range_adaptor_closure<pipe<Lhs, Rhs>> {
[[no_unique_address]] Lhs lhs;
[[no_unique_address]] Rhs rhs;
constexpr pipe(Lhs _lhs, Rhs _rhs) noexcept(NO_EXCEPT) : lhs(std::move(_lhs)), rhs(std::move(_rhs)) {}
template<class Range>
requires pipe_invocable<const Lhs &, const Rhs &, Range>
inline constexpr auto operator()(Range&& range) const noexcept(NO_EXCEPT) {
return rhs(lhs(std::forward<Range>(range)));
}
static constexpr bool has_simple_call_op = true;
};
} // namespace views::adaptor
} // namespace uni
#line 28 "iterable/operation.hpp"
#line 2 "iterable/z_array.hpp"
#line 6 "iterable/z_array.hpp"
#line 9 "iterable/z_array.hpp"
#line 2 "adaptor/valarray.hpp"
#line 11 "adaptor/valarray.hpp"
#line 14 "adaptor/valarray.hpp"
#line 16 "adaptor/valarray.hpp"
namespace uni {
template<class T> struct valarray : internal::advanced_container<std::valarray<T>> {
private:
using base = internal::advanced_container<std::valarray<T>>;
public:
using size_type = internal::size_t;
using iterator = T*;
using const_iterator = const T*;
protected:
inline bool _validate_index_in_right_open([[maybe_unused]] const size_type p) const noexcept(NO_EXCEPT) {
return 0 <= p and p < this->size();
}
inline bool _validate_index_in_closed([[maybe_unused]] const size_type p) const noexcept(NO_EXCEPT) {
return 0 <= p and p <= this->size();
}
inline bool _validate_rigth_open_interval([[maybe_unused]] const size_type l, [[maybe_unused]] const size_type r) const noexcept(NO_EXCEPT) {
return 0 <= l and l <= r and r <= this->size();
}
inline size_type _positivize_index(const size_type p) const noexcept(NO_EXCEPT) {
return p < 0 ? this->size() + p : p;
}
public:
valarray() noexcept(NO_EXCEPT) {}
explicit valarray(const std::size_t length, const T& val = T{}) noexcept(NO_EXCEPT) : base(val, length) {}
template<std::input_iterator I, std::sentinel_for<I> S>
valarray(I first, S last) noexcept(NO_EXCEPT) : base(std::ranges::distance(first, last)) { std::ranges::copy(first, last, std::ranges::begin(*this)); }
template<class U> valarray(const U* pointer, const size_t n) noexcept(NO_EXCEPT) : base(pointer, n) {};
valarray(const std::slice_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::gslice_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::mask_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::indirect_array<T>& arr) noexcept(NO_EXCEPT) : base(arr) {};
valarray(const std::initializer_list<T>& init) noexcept(NO_EXCEPT) : base(init) {}
valarray(const internal::advanced_container<std::valarray<T>>& arr) noexcept(NO_EXCEPT) : base(arr) {}
#ifdef __GNUC__
template<class Dom> valarray(const std::_Expr<Dom,T>& expr) noexcept(NO_EXCEPT) : base(expr) {}
#endif
inline auto size() const noexcept(NO_EXCEPT) { return static_cast<size_type>(this->base::size()); }
inline void reserve(const size_type) noexcept(NO_EXCEPT) { /* do nothing */ }
template<std::input_iterator I, std::sentinel_for<I> S>
inline void assign(I first, S last) noexcept(NO_EXCEPT) {
this->resize(std::ranges::distance(first, last));
std::ranges::copy(first, last, std::ranges::begin(*this));
}
inline void assign(const std::size_t length, const T& val = T{}) noexcept(NO_EXCEPT) {
this->base::resize(length, val);
}
inline void resize(const std::size_t length, const T& val = T{}) noexcept(NO_EXCEPT) {
base temp = *this;
this->assign(length, val);
std::move(std::begin(temp), std::min(std::end(temp), std::next(std::begin(temp), length)), std::begin(*this));
}
inline const T& operator[](size_type pos) const noexcept(NO_EXCEPT) {
pos = this->_positivize_index(pos), assert(this->_validate_index_in_right_open(pos));
return this->base::operator[](pos);
}
inline T& operator[](size_type pos) noexcept(NO_EXCEPT) {
pos = this->_positivize_index(pos), assert(this->_validate_index_in_right_open(pos));
return this->base::operator[](pos);
}
inline const T& back() const noexcept(NO_EXCEPT) { return *std::prev(this->end()); }
inline T& back() noexcept(NO_EXCEPT) { return *std::prev(this->end()); }
inline const T& front() const noexcept(NO_EXCEPT) { return *this->begin(); }
inline T& front() noexcept(NO_EXCEPT) { return *this->begin(); }
inline auto rbegin() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::end(*this)); }
inline auto rend() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::begin(*this)); }
inline auto rbegin() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::end(*this)); }
inline auto rend() const noexcept(NO_EXCEPT) { return std::make_reverse_iterator(std::ranges::begin(*this)); }
};
} // namespace uni
#line 11 "iterable/z_array.hpp"
namespace uni {
// Thanks to: atcoder::z_algorithm
template<class SizeType = internal::size_t, class Container = valarray<SizeType>>
struct z_array : Container {
using size_type = SizeType;
template<std::input_iterator I, std::sentinel_for<I> S>
z_array(I first, S last) : Container(std::ranges::distance(first, last), {}) {
const size_type n = static_cast<size_type>(std::ranges::distance(first, last));
if(n == 0) return;
for(size_type i = 1, j = 0; i < n; ++i) {
size_type& k = this->operator[](i);
k = (j + this->operator[](j) <= i) ? 0 : std::ranges::min(j + this->operator[](j) - i, this->operator[](i - j));
while(i + k < n and first[k] == first[i + k]) ++k;
if(j + this->operator[](j) < i + this->operator[](i)) j = i;
}
*this->begin() = n;
}
template<std::ranges::input_range R>
explicit z_array(R&& range) : z_array(ALL(range)) {}
};
} // namespace uni
#line 31 "iterable/operation.hpp"
#line 2 "view/concat.hpp"
#line 11 "view/concat.hpp"
#line 18 "view/concat.hpp"
namespace uni {
namespace internal {
namespace view_impl {
template<std::ranges::input_range V0, std::ranges::input_range V1>
requires std::ranges::view<V0> && std::ranges::view<V1>
struct concat_view : std::ranges::view_interface<concat_view<V0, V1>> {
private:
V0 _b0;
V1 _b1;
template<bool Const> using B0 = internal::maybe_const_t<Const, V0>;
template<bool Const> using B1 = internal::maybe_const_t<Const, V1>;
template<bool Const> struct iterator_tag {};
template<bool Const>
requires std::ranges::forward_range<B0<Const>> && std::ranges::forward_range<B1<Const>>
struct iterator_tag<Const> {
public:
using iterator_category = uni::internal::most_primitive_iterator_tag<
typename std::iterator_traits<std::ranges::iterator_t<B0<Const>>>::iterator_category,
typename std::iterator_traits<std::ranges::iterator_t<B1<Const>>>::iterator_category
>;
};
public:
template<bool> class iterator;
constexpr explicit concat_view(V0 v0, V1 v1) noexcept(NO_EXCEPT)
: _b0(std::move(v0)), _b1(std::move(v1))
{}
inline constexpr std::pair<V0, V1> base() const & noexcept(NO_EXCEPT)
requires std::copy_constructible<V0> && std::copy_constructible<V0>
{
return { this->_b0, this->_b1 };
}
inline constexpr std::pair<V0,V1> base() && noexcept(NO_EXCEPT) {
return { std::move(this->_b0), std::move(this->_b1) };
}
inline constexpr auto begin() noexcept(NO_EXCEPT)
requires (!internal::simple_view<V0> && !internal::simple_view<V1>)
{
return iterator<false>(this, std::ranges::begin(this->_b0), std::ranges::begin(this->_b1), 0);
}
inline constexpr auto begin() const noexcept(NO_EXCEPT)
requires std::ranges::range<const V0> && std::ranges::range<const V1>
{
return iterator<true>(this, std::ranges::begin(this->_b0), std::ranges::begin(this->_b1), 0);
}
inline constexpr auto end() noexcept(NO_EXCEPT)
requires (!internal::simple_view<V0> && !internal::simple_view<V1>)
{
if constexpr(std::ranges::common_range<V0> && std::ranges::common_range<V1>) {
return iterator<false>(this, std::ranges::end(this->_b0), std::ranges::end(this->_b1), 1);
}
else {
return std::default_sentinel;
}
}
inline constexpr auto end() const noexcept(NO_EXCEPT)
requires std::ranges::range<const V0> && std::ranges::range<const V1>
{
if constexpr(std::ranges::common_range<const V0> && std::ranges::common_range<const V1>) {
return iterator<true>(this, std::ranges::end(this->_b0), std::ranges::end(this->_b1), 1);
}
else {
return std::default_sentinel;
}
}
inline constexpr auto size() noexcept(NO_EXCEPT)
requires std::ranges::sized_range<V0> && std::ranges::sized_range<V1>
{
return static_cast<std::size_t>(std::ranges::distance(this->_b0) + std::ranges::distance(this->_b1));
}
inline constexpr auto size() const noexcept(NO_EXCEPT)
requires std::ranges::sized_range<const V0> && std::ranges::sized_range<const V1>
{
return static_cast<std::size_t>(std::ranges::distance(this->_b0) + std::ranges::distance(this->_b1));
}
};
template<std::ranges::input_range V0, std::ranges::input_range V1>
requires std::ranges::view<V0> && std::ranges::view<V1>
template<bool Const>
struct concat_view<V0, V1>::iterator : iterator_tag<Const> {
private:
using Parent = internal::maybe_const_t<Const, concat_view>;
using B0 = concat_view::B0<Const>;
using B1 = concat_view::B1<Const>;
std::ranges::iterator_t<B0> _c0 = std::ranges::iterator_t<B0>();
std::ranges::iterator_t<B0> _b0 = std::ranges::iterator_t<B0>();
std::ranges::sentinel_t<B0> _e0 = std::ranges::sentinel_t<B0>();
std::ranges::iterator_t<B1> _c1 = std::ranges::iterator_t<B1>();
std::ranges::iterator_t<B1> _b1 = std::ranges::iterator_t<B1>();
std::ranges::sentinel_t<B1> _e1 = std::ranges::sentinel_t<B1>();
int _block = 0;
constexpr iterator(Parent *const parent, const std::ranges::iterator_t<B0> c0, const std::ranges::iterator_t<B1> c1, const int block) noexcept(NO_EXCEPT)
: _c0(std::move(c0)), _b0(std::ranges::begin(parent->_b0)), _e0(std::ranges::end(parent->_b0)),
_c1(std::move(c1)), _b1(std::ranges::begin(parent->_b1)), _e1(std::ranges::end(parent->_b1)),
_block(block || std::ranges::empty(parent->_b0))
{}
friend concat_view;
public:
using difference_type = std::common_type_t<std::ranges::range_difference_t<B0>, std::ranges::range_difference_t<B1>>;
using value_type = std::common_type_t<std::ranges::range_value_t<B0>, std::ranges::range_value_t<B1>>;
using reference_type = std::common_reference_t<std::ranges::range_reference_t<B0>, std::ranges::range_reference_t<B1>>;
using iterator_concept = most_primitive_iterator_concept<Const, V0, V1>;
iterator() noexcept(NO_EXCEPT)
requires std::default_initializable<std::ranges::iterator_t<B0>> &&
std::default_initializable<std::ranges::iterator_t<B0>>
= default;
constexpr iterator(iterator<!Const> itr) noexcept(NO_EXCEPT)
requires
Const &&
std::convertible_to<std::ranges::iterator_t<V0>, std::ranges::iterator_t<B0>> &&
std::convertible_to<std::ranges::sentinel_t<V0>, std::ranges::sentinel_t<B0>> &&
std::convertible_to<std::ranges::iterator_t<V1>, std::ranges::iterator_t<B1>> &&
std::convertible_to<std::ranges::sentinel_t<V1>, std::ranges::sentinel_t<B1>>
: _c0(std::move(itr._c0)), _b0(std::move(itr._b0)), _e0(std::move(itr._e0)),
_c1(std::move(itr._c0)), _b1(std::move(itr._b0)), _e1(std::move(itr._e1)),
_block(itr._block)
{}
inline constexpr std::variant<std::ranges::iterator_t<B0>, std::ranges::iterator_t<B1>>
base() && noexcept(NO_EXCEPT) {
if(this->_block == 0) return std::move(this->_c0);
else return std::move(this->_C1);
}
inline constexpr
std::variant<
std::reference_wrapper<const std::ranges::iterator_t<B0>>,
std::reference_wrapper<const std::ranges::iterator_t<B1>>
>
base() const & noexcept {
if(this->_block == 0) return std::move(this->_c0);
else return std::move(this->_c1);
}
inline constexpr reference_type operator*() const noexcept(NO_EXCEPT)
{
if(this->_block == 0) return *this->_c0;
else return *this->_c1;
}
inline constexpr iterator& operator++() noexcept(NO_EXCEPT)
{
assert(this->_c0 != this->_e0 or this->_c1 != this->_e1);
if(this->_block == 0) {
if(++this->_c0 == this->_e0) {
this->_block = 1;
assert(this->_c1 == this->_b1);
}
}
else {
++this->_c1;
}
return *this;
}
inline constexpr void operator++(int) noexcept(NO_EXCEPT) { ++*this; }
inline constexpr iterator operator++(int) noexcept(NO_EXCEPT)
requires std::ranges::forward_range<B0> && std::ranges::forward_range<B1>
{
const auto res = *this; ++*this; return res;
}
inline constexpr iterator& operator--() noexcept(NO_EXCEPT)
requires
std::ranges::bidirectional_range<B0> && std::ranges::bidirectional_range<B1> &&
std::bidirectional_iterator<std::ranges::sentinel_t<B0>>
{
if(this->_block == 1) {
if(this->_c1 == this->_b1) {
this->_block = 0;
this->_c0 = std::ranges::prev(this->_e0);
}
else {
--this->_c1;
}
}
else {
--this->_c0;
}
return *this;
}
inline constexpr iterator operator--(int) noexcept(NO_EXCEPT)
requires std::ranges::bidirectional_range<B0> && std::ranges::bidirectional_range<B1>
{
const auto res = *this; --*this; return res;
}
inline constexpr iterator& operator+=(const difference_type diff) noexcept(NO_EXCEPT)
requires
std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
if(diff > 0) {
if(this->_block == 0) {
const auto missing = std::ranges::advance(this->_c0, diff, this->_e0);
if(this->_c0 == this->_e0) {
this->_block = 1;
assert(this->_c1 == this->_b1);
std::ranges::advance(this->_c1, missing, this->_e1);
}
}
else {
std::ranges::advance(this->_c1, diff, this->_e1);
}
}
if(diff < 0) {
if(this->_block == 1) {
const auto missing = std::ranges::advance(this->_c1, diff, this->_b1);
if(missing < 0) {
this->_block = 0;
assert(this->_c0 == this->_e0);
std::ranges::advance(this->_c0, missing, this->_b0);
}
}
else {
std::ranges::advance(this->_c0, diff, this->_b0);
}
}
return *this;
}
inline constexpr iterator& operator-=(const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
return *this += -diff;
}
inline constexpr decltype(auto) operator[](const difference_type diff) const noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
return *(*this + diff);
}
friend inline constexpr bool operator==(const iterator& lhs, std::default_sentinel_t) noexcept(NO_EXCEPT)
{
if(lhs._block == 0) return false;
if(lhs._block == 1) return lhs._c1 == lhs._e1;
assert(false);
}
friend inline constexpr bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::equality_comparable<std::ranges::iterator_t<B0>> &&
std::equality_comparable<std::ranges::iterator_t<B1>>
{
if(lhs._block != rhs._block) return false;
return lhs._block == 0 ? lhs._c0 == rhs._c0 : lhs._c1 == rhs._c1;
}
friend inline constexpr auto operator<=>(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
if(lhs._block != rhs._block) return lhs._block <=> rhs._block;
return lhs._block == 0 ? lhs._c0 <=> rhs._c0 : lhs._c1 <=> rhs._c1;
}
friend inline constexpr iterator operator+(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
auto res = itr; res += diff; return res;
}
friend inline constexpr iterator operator+(const difference_type diff, const iterator& itr) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
return itr + diff;
}
friend inline constexpr iterator operator-(const iterator& itr, const difference_type diff) noexcept(NO_EXCEPT)
requires std::ranges::random_access_range<B0> && std::ranges::random_access_range<B1>
{
auto res = itr; res -= diff; return res;
}
friend inline constexpr const difference_type operator-(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::sized_sentinel_for<std::ranges::iterator_t<B0>, std::ranges::iterator_t<B0>> &&
std::sized_sentinel_for<std::ranges::iterator_t<B1>, std::ranges::iterator_t<B1>>
{
if(lhs._block == rhs._block) {
return lhs._block == 0 ? std::ranges::distance(rhs._c0, lhs._c0) : std::ranges::distance(rhs._c1, lhs._c1);
}
if(lhs._block > rhs._block) return std::ranges::distance(rhs._c0, rhs._e0) + std::ranges::distance(lhs._b1, lhs._c1);
if(lhs._block < rhs._block) return -(rhs - lhs);
assert(false);
}
friend inline constexpr const difference_type operator-(std::default_sentinel_t, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::sized_sentinel_for<std::ranges::sentinel_t<B0>, std::ranges::iterator_t<B0>> &&
std::sized_sentinel_for<std::ranges::sentinel_t<B1>, std::ranges::iterator_t<B1>>
{
if(rhs._block == 0) return std::ranges::distance(rhs._c0, rhs._e0) + std::ranges::distance(rhs._b1, rhs._e1);
if(rhs._block == 1) return std::ranges::distance(rhs._c1, rhs._e1);
assert(false);
}
friend inline constexpr const difference_type operator-(const iterator& lhs, std::default_sentinel_t rhs) noexcept(NO_EXCEPT)
requires
std::sized_sentinel_for<std::ranges::sentinel_t<B0>, std::ranges::iterator_t<B0>> &&
std::sized_sentinel_for<std::ranges::sentinel_t<B1>, std::ranges::iterator_t<B1>>
{
return -(rhs - lhs);
}
friend inline constexpr
std::common_reference_t<
std::ranges::range_rvalue_reference_t<B0>,
std::ranges::range_rvalue_reference_t<B1>
>
iter_move(const iterator& itr) noexcept(NO_EXCEPT)
{
if(itr._block == 0) return std::ranges::iter_move(itr._c0);
if(itr._block == 1) return std::ranges::iter_move(itr._c1);
assert(false);
}
friend inline constexpr void iter_swap(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT)
requires
std::indirectly_swappable<std::ranges::iterator_t<B0>> &&
std::indirectly_swappable<std::ranges::iterator_t<B1>> &&
std::indirectly_swappable<std::ranges::iterator_t<B0>, std::ranges::iterator_t<B1>>
{
if(lhs._block == 0 && rhs._block == 0) std::ranges::iter_swap(lhs._c0, rhs._c0);
if(lhs._block == 0 && rhs._block == 1) std::ranges::iter_swap(lhs._c0, rhs._c1);
if(lhs._block == 1 && rhs._block == 0) std::ranges::iter_swap(lhs._c1, rhs._c0);
if(lhs._block == 1 && rhs._block == 1) std::ranges::iter_swap(lhs._c1, rhs._c1);
assert(false);
}
};
} // namespace view_impl
} // namespace internal
template<class...> struct concat_view;
template<class T>
struct concat_view<T> : std::views::all_t<T> {
using std::views::all_t<T>::all_t;
};
template<class T0, class T1>
struct concat_view<T0, T1> : internal::view_impl::concat_view<std::views::all_t<T0>, std::views::all_t<T1>> {
explicit concat_view(T0&& v0, T1&& v1) noexcept(NO_EXCEPT)
: internal::view_impl::concat_view<std::views::all_t<T0>, std::views::all_t<T1>>(std::forward<T0>(v0), std::forward<T1>(v1))
{}
};
template<class T0, class T1, class... Ts>
struct concat_view<T0, T1, Ts...> : concat_view<concat_view<T0, T1>, Ts...> {
explicit concat_view(T0&& v0, T1&& v1, Ts&&... vs) noexcept(NO_EXCEPT)
: concat_view<concat_view<T0, T1>, Ts...>(
concat_view<T0, T1>(std::forward<T0>(v0), std::forward<T1>(v1)), std::forward<Ts>(vs)...
)
{}
};
namespace views {
namespace internal {
template<class... Ts>
concept can_concat_view = requires { concat_view<Ts...>(std::declval<Ts>()...); };
} // namespace internal
struct Concat {
template<class... Ts>
requires (sizeof...(Ts) == 0 || internal::can_concat_view<Ts...>)
inline constexpr auto operator() [[nodiscard]] (Ts&&... vs) const {
if constexpr(sizeof...(Ts) == 0) return std::views::empty<std::nullptr_t>;
else return concat_view<std::views::all_t<Ts>...>(std::forward<Ts>(vs)...);
}
};
inline constexpr Concat concat;
} // namespace views
} // namespace uni.
namespace std::ranges {
template<class... Views>
inline constexpr bool enable_borrowed_range<uni::concat_view<Views...>> = (enable_borrowed_range<Views> && ...);
}
#line 2 "global/constants.hpp"
#line 7 "global/constants.hpp"
#include <cmath>
#line 11 "global/constants.hpp"
#line 14 "global/constants.hpp"
#line 2 "numeric/limits.hpp"
#line 6 "numeric/limits.hpp"
#line 9 "numeric/limits.hpp"
#line 11 "numeric/limits.hpp"
namespace uni {
template<class T>
struct numeric_limits : std::numeric_limits<T> {
static constexpr long double FLOAT_EPSILON = 1E-14;
static constexpr T arithmetic_infinity() noexcept(NO_EXCEPT) {
return std::numeric_limits<T>::max() / 2 - 1;
}
static constexpr T arithmetic_negative_infinity() noexcept(NO_EXCEPT) {
return std::numeric_limits<T>::lowest() / 2 + 1;
}
static constexpr T arithmetic_epsilon() noexcept(NO_EXCEPT) {
if constexpr(std::is_floating_point_v<T>) {
return numeric_limits::FLOAT_EPSILON;
}
else {
return 0;
}
}
};
constexpr i32 INF32 = numeric_limits<i32>::arithmetic_infinity();
constexpr i64 INF64 = numeric_limits<i64>::arithmetic_infinity();
template<class T>
constexpr T INF = numeric_limits<T>::arithmetic_infinity();
template<class T>
constexpr T EPSILON = numeric_limits<T>::arithmetic_epsilon();
} // namespace uni
#line 16 "global/constants.hpp"
namespace uni {
namespace internal {
template<class T>
consteval auto get_pi() {
if constexpr(std::integral<T>) {
return static_cast<T>(3);
}
else if constexpr(std::same_as<T, float>) {
return M_PIf;
}
else if constexpr(std::same_as<T, double>) {
return M_PI;
}
else if constexpr(std::same_as<T, ld>) {
return M_PIl;
}
else {
static_assert(EXCEPTION_ON_TYPE<T>);
}
}
} // namespace internal
template<class T = ld>
constexpr auto PI = internal::get_pi<T>();
enum class comparison : std::uint8_t {
equal_to,
not_equal_to,
equals = equal_to,
eq = equal_to,
under,
over,
or_under,
or_over,
less = under,
more = over,
less_than = under,
more_than = over,
not_less_than = or_over,
not_more_than = or_under,
leq = or_under,
geq = or_over
};
enum class interval_notation : std::uint8_t {
right_open,
left_open,
open,
closed,
};
enum class replacement_policy : std::uint8_t {
insert_sync,
overwrite_sync,
overwrite_async
};
enum class rotation : std::int8_t {
clockwise,
counter_clockwise,
anti_clockwise = counter_clockwise,
};
enum class positional_relation : std::int8_t {
clockwise,
counter_clockwise,
anti_clockwise = counter_clockwise,
backward,
forward,
in,
on,
out,
included = in,
inscribed,
intersecting,
circumscribed,
distant,
};
enum class alignment : std::int8_t {
left,
center,
right
};
} // namespace uni
#line 35 "iterable/operation.hpp"
namespace uni {
template<std::ranges::input_range R0, std::ranges::input_range R1>
requires std::constructible_from<
R0, std::common_type_t<std::ranges::range_size_t<R0>,std::ranges::range_size_t<R1>>
>
R0 concat(R0&& r0, R1&& r1) noexcept(NO_EXCEPT) {
R0 res(std::ranges::size(r0) + std::ranges::size(r1));
std::ranges::copy(r0, std::ranges::begin(res));
std::ranges::copy(r1, std::ranges::next(std::ranges::begin(res), std::ranges::size(r0)));
return res;
}
template<std::ranges::input_range R, std::ranges::input_range... Rs>
R concat(R&& range, Rs&&... tails) noexcept(NO_EXCEPT) {
return uni::concat(range, uni::concat(tails...));
}
template<std::ranges::input_range R>
requires
requires(R r) {
r.erase(std::ranges::unique(ALL(r)), std::ranges::end(r));
}
inline auto unique(R range) noexcept(NO_EXCEPT) {
std::ranges::sort(range);
range.erase(std::ranges::unique(ALL(range)), std::ranges::end(range));
return range;
}
template<
std::input_iterator I,
std::sentinel_for<I> S,
class T = std::iter_value_t<I>
>
T mex(I first, S last, const T& base = T()) noexcept(NO_EXCEPT) {
std::vector<T> val(first, last);
std::ranges::sort(val);
{
auto range = std::ranges::unique(val);
val.erase(ALL(range));
}
val.erase(val.begin(), std::ranges::lower_bound(val, base));
T i = 0;
while(i < std::ranges::ssize(val) && val[i] == i + base) ++i;
return T{i} + base;
}
template<std::ranges::input_range R>
auto mex(R&& range, const std::ranges::range_value_t<R>& base = std::ranges::range_value_t<R>()) noexcept(NO_EXCEPT) {
return mex(ALL(range), base);
}
template<class T>
auto mex(const std::initializer_list<T> v, const T& base = T()) noexcept(NO_EXCEPT) {
return mex(ALL(v), base);
}
template<std::input_iterator I, std::sentinel_for<I> S, class T>
inline constexpr auto gcd(I first, S last) noexcept(NO_EXCEPT) {
T res = T{0};
for(auto itr=first; itr!=last; ++itr) res = std::gcd(res, *itr);
return res;
}
template<std::input_iterator I, std::sentinel_for<I> S, class T>
inline constexpr auto lcm(I first, S last) noexcept(NO_EXCEPT) {
T res = T{1};
for(auto itr=first; itr!=last; ++itr) res = std::lcm(res, *itr);
return res;
}
template<std::ranges::input_range R, class T = std::ranges::range_value_t<R>>
auto mex(R&& range, const T& base) noexcept(NO_EXCEPT) {
return mex(ALL(range), base);
}
template<std::ranges::input_range R>
auto gcd(R&& range) noexcept(NO_EXCEPT) {
return gcd(ALL(range));
}
template<std::ranges::input_range R>
auto lcm(R&& range) noexcept(NO_EXCEPT) {
return lcm(ALL(range));
}
template<class R, std::input_iterator I, std::sentinel_for<I> S, class D>
requires
requires (R r, I itr) {
r.emplace_back(itr, itr);
}
auto split(I first, S last, const D& delim = ' ') noexcept(NO_EXCEPT) {
R res;
for(auto itr=first, fnd=first; ; itr=std::ranges::next(fnd)) {
fnd = std::find(itr, last, delim);
res.emplace_back(itr, fnd);
if(fnd == last) break;
}
return res;
}
template<class R, std::ranges::input_range V, class D>
requires (!std::ranges::input_range<D>)
auto split(V&& v, D&& d) noexcept(NO_EXCEPT) { return split<R>(ALL(v), d); }
template<class R, std::ranges::input_range V, std::ranges::input_range Ds>
auto split(V&& v, Ds&& ds) noexcept(NO_EXCEPT) {
R res = { v };
ITR(d, ds) {
R tmp;
ITR(p, res) tmp = concat(tmp, split<R>(p, d));
res = std::move(tmp);
}
return res;
}
template<class R, std::ranges::input_range V, class T>
auto split(V&& v, const std::initializer_list<T> ds) noexcept(NO_EXCEPT){
return split<R,V>(v, std::vector<T>(ALL(ds)));
}
template<std::ranges::sized_range Source, std::ranges::sized_range Qeury>
auto find(Source&& source, Qeury&& query) noexcept(NO_EXCEPT) {
z_array z_arr(views::concat(query, source));
const auto query_size = std::ranges::ssize(query);
vector<std::ranges::iterator_t<Source>> res;
{
auto itr = std::ranges::begin(source);
REP(i, query_size, std::ranges::size(z_arr)) {
if(z_arr[i] >= query_size) res.push_back(itr);
++itr;
}
}
return res;
}
template<
replacement_policy POLICY,
std::ranges::sized_range R,
std::ranges::sized_range From,
std::ranges::sized_range To
>
auto replaced(R&& source, From&& from, To&& to) noexcept(NO_EXCEPT) {
std::remove_cvref_t<R> res;
if constexpr(POLICY == replacement_policy::insert_sync) {
const auto found = find(source, from);
auto itr = std::ranges::begin(source);
ITRR(fn, found) {
std::ranges::copy(itr, fn, std::back_inserter(res));
std::ranges::copy(ALL(to), std::back_inserter(res));
itr = std::ranges::next(fn, std::ranges::size(from));
}
std::ranges::copy(itr, std::ranges::end(source), std::back_inserter(res));
}
else {
res = source;
res.resize(std::ranges::size(source) + std::ranges::size(to));
const auto found = find(res, from);
auto prev = std::ranges::begin(res);
ITRR(fn, found) {
if constexpr(POLICY == replacement_policy::overwrite_sync) {
if(prev <= fn) prev = std::ranges::copy(to, fn);
}
else {
std::ranges::copy(to, fn);
}
}
res.resize(std::ranges::size(source));
}
return res;
}
template<
std::ranges::sized_range R,
std::ranges::sized_range From,
std::ranges::sized_range To
>
inline auto replaced(R&& source, From&& from, To&& to) noexcept(NO_EXCEPT) {
return replaced<replacement_policy::insert_sync, R, From, To>(std::forward<R>(source), std::forward<From>(from), std::forward<To>(to));
}
template<alignment ALIGNMENT, internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto align(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
if(std::ssize(source) >= size) return source;
if(ALIGNMENT == alignment::left) {
R left, right;
left = source;
right.resize(size - std::size(left), v);
return R(ALL(uni::views::concat(left, right)));
}
if(ALIGNMENT == alignment::center) {
R left, center, right;
center = source;
left.resize((size - std::size(center)) / 2, v);
right.resize(size - std::size(center) - std::size(left), v);
return R(ALL(uni::views::concat(left, center, right)));
}
if(ALIGNMENT == alignment::right) {
R left, right;
right = source;
left.resize(size - std::size(right), v);
return R(ALL(uni::views::concat(left, right)));
}
assert(false);
}
template<internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto ljust(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
return align<alignment::left>(source, size, v);
}
template<internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto cjust(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
return align<alignment::center>(source, size, v);
}
template<internal::resizable_range R, class T = std::ranges::range_value_t<R>>
auto rjust(R&& source, const internal::size_t size, const T& v = T()) noexcept(NO_EXCEPT) {
return align<alignment::right>(source, size, v);
}
template<
class Res,
std::ranges::random_access_range Target,
std::ranges::forward_range Order
>
requires std::ranges::output_range<Res, std::ranges::range_value_t<Target>>
Res ordered_by(Target&& target, Order&& order) noexcept(NO_EXCEPT) {
const auto target_size = std::ranges::ssize(target);
const auto order_size = std::ranges::ssize(order);
Res res(order_size);
{
auto res_itr = std::ranges::begin(res);
auto order_itr = std::ranges::begin(order);
const auto order_end = std::ranges::end(std::forward<Order>(order));
for(; order_itr != order_end; ++res_itr, ++order_itr) {
if constexpr(std::signed_integral<std::ranges::range_value_t<Order>>) assert(0 <= *order_itr);
assert(*order_itr < target_size);
*res_itr = target[*order_itr];
}
}
return res;
}
template<
std::ranges::random_access_range Target,
std::ranges::forward_range Order
>
auto ordered_by(Target&& target, Order&& order) noexcept(NO_EXCEPT) {
return ordered_by<std::remove_cvref_t<Target>, Target, Order>(std::forward<Target>(target), std::forward<Order>(order));
}
template<std::ranges::input_range Target, std::ranges::input_range Source>
requires std::equality_comparable_with<std::ranges::range_value_t<Target>, std::ranges::range_value_t<Source>>
auto is_subsequence_of(Target&& target, Source&& source) noexcept(NO_EXCEPT) {
auto target_itr = std::ranges::begin(source);
auto source_itr = std::ranges::begin(source);
const auto target_end = std::ranges::end(source);
const auto source_end = std::ranges::end(source);
for(; source_itr != source_end; ++source_itr) {
if(*target_itr == *source_itr) ++target_itr;
}
return target_itr == target_end;
}
template<std::ranges::input_range Target, std::ranges::input_range Source>
requires std::equality_comparable_with<std::ranges::range_value_t<Target>, std::ranges::range_value_t<Source>>
auto is_continuous_subsequence_of(Target&& target, Source&& source) noexcept(NO_EXCEPT) {
auto found = find(source, target);
return found.size() > 0;
}
} // namespace uni
#line 31 "numeric/arithmetic.hpp"
namespace uni {
template<class T>
inline constexpr T div_floor(const T& x, const T& d) noexcept(NO_EXCEPT) {
if constexpr(std::is_integral_v<T>) {
return x / d - (x % d && ((x < 0) ^ (d < 0)));
}
else {
return std::floor(x / d);
}
}
template<class T>
inline constexpr T div_ceil(const T& x, const T& d) noexcept(NO_EXCEPT) {
if constexpr(std::is_integral_v<T>) {
return div_floor(x + d - 1, d);
}
else {
return std::ceil(x / d);
}
}
template<class T>
inline constexpr T div_round(const T& x, const T& d) noexcept(NO_EXCEPT) {
if constexpr(std::is_integral_v<T>) {
return div_round<ld>(x, d);
}
else {
return std::round(x / d);
}
}
template<class T>
inline constexpr std::make_signed_t<T> to_signed(const T& x) noexcept(NO_EXCEPT) {
return std::bit_cast<std::make_signed_t<T>>(x);
}
template<class T>
inline constexpr std::make_unsigned_t<T> to_unsigned(const T& x) noexcept(NO_EXCEPT) {
return std::bit_cast<std::make_unsigned_t<T>>(x);
}
namespace internal {
template<class T>
inline constexpr auto perm(const T& n, const T& r) noexcept(NO_EXCEPT) {
T res = 1;
REP(i, r) res *= n - i;
return res;
}
template<class T>
inline constexpr auto comb(const T& n, T r) noexcept(NO_EXCEPT) {
if(n < 2 * r) r = n - r;
T p = 1, q = 1;
REP(i, r) p *= n - i, q *= r - i;
return p / q;
}
} // namespace internal
template<class T0, std::common_with<T0> T1>
inline constexpr auto perm(const T0& n, const T1& r) noexcept(NO_EXCEPT) {
assert(n >= 0), assert(r >= 0);
using T = std::common_type_t<T0, T1>;
if(n < r) return static_cast<T>(0);
return internal::perm<T>(n, r);
}
template<class T0, std::common_with<T0> T1>
inline constexpr auto comb(const T0& n, const T1& r) noexcept(NO_EXCEPT) {
assert(n >= 0), assert(r >= 0);
using T = std::common_type_t<T0, T1>;
if(n < r) return static_cast<T>(0);
if(n == r) return static_cast<T>(1);
return internal::comb<T>(n, r);
}
template<class T, class U, std::invocable<T, T> F = std::multiplies<>>
constexpr T pow(T x, U n, F mul = F(), T one = static_cast<T>(1)) noexcept(NO_EXCEPT) {
if(n == 0) return one;
if(n == 1 || x == one) return x;
T res = one;
while(true) {
if(n & 1) res = mul(res, x);
x = mul(x, x);
if(n == 0) return res;
n >>= 1;
}
assert(false);
}
using atcoder::pow_mod;
using atcoder::inv_mod;
using atcoder::crt;
template<class T> inline constexpr T sign(const T& x) noexcept(NO_EXCEPT) {
if(x == 0) return 0;
return (x > 0) ? 1 : -1;
}
template<class T, T FROM_MIN, T FROM_MAX, T TO_MIN, T TO_MAX> inline constexpr T mapping(const T x) {
return (x - FROM_MIN) * (TO_MAX - TO_MIN) / (FROM_MAX - FROM_MIN) + TO_MIN;
}
template<class T> inline constexpr T mapping(const T x, const T from_min, const T from_max, const T to_min, const T to_max) {
return (x - from_min) * (to_max - to_min) / (from_max - from_min) + to_min;
}
template<class... Args>
inline constexpr std::common_type_t<Args...> min(const Args&... args) noexcept(NO_EXCEPT) {
return std::min({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<class... Args>
inline constexpr std::common_type_t<Args...> max(const Args&... args) noexcept(NO_EXCEPT) {
return std::max({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<class T>
inline constexpr T gcd(const std::initializer_list<T> args) noexcept(NO_EXCEPT) {
return gcd(ALL(args));
}
template<class... Args>
inline constexpr std::common_type_t<Args...> gcd(const Args&... args) noexcept(NO_EXCEPT) {
return gcd({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<class T>
inline constexpr T lcm(const std::initializer_list<T> args) noexcept(NO_EXCEPT) {
return lcm(ALL(args));
}
template<class... Args>
inline constexpr std::common_type_t<Args...> lcm(const Args&... args) noexcept(NO_EXCEPT) {
return lcm({ static_cast<std::common_type_t<Args...>>(args)... });
}
template<std::integral T0, std::integral T1>
inline constexpr std::optional<std::common_type_t<T0, T1>> add_overflow(const T0& a, const T1& b) noexcept(NO_EXCEPT) {
std::common_type_t<T0, T1> res;
if(__builtin_add_overflow(a, b, &res)) return {};
return res;
}
template<std::integral T0, std::integral T1>
inline constexpr std::optional<std::common_type_t<T0, T1>> sub_overflow(const T0& a, const T1& b) noexcept(NO_EXCEPT) {
std::common_type_t<T0, T1> res;
if(__builtin_sub_overflow(a, b, &res)) return {};
return res;
}
template<std::integral T0, std::integral T1>
inline constexpr std::optional<std::common_type_t<T0, T1>> mul_overflow(const T0& a, const T1& b) noexcept(NO_EXCEPT) {
std::common_type_t<T0, T1> res;
if(__builtin_mul_overflow(a, b, &res)) return {};
return res;
}
template<std::integral T0, std::integral T1, std::integral Limit>
inline auto add_clamp(const T0 x, const T1 y, const Limit inf, const Limit sup) noexcept(NO_EXCEPT) {
using Common = std::common_type_t<T0, T1, Limit>;
const auto res = add_overflow<Common>(x, y);
if(!res) {
if(x < 0 && y < 0) return inf;
if(x > 0 && y > 0) return sup;
assert(false);
}
return std::clamp<Common>(*res, inf, sup);
}
template<std::integral T0, std::integral T1, std::integral Limit>
inline auto sub_clamp(const T0 x, const T1 y, const Limit inf, const Limit sup) noexcept(NO_EXCEPT) {
using Common = std::common_type_t<T0, T1, Limit>;
const auto res = sub_overflow<Common>(x, y);
if(!res) {
if(x < 0 && y > 0) return inf;
if(x > 0 && y < 0) return sup;
assert(false);
}
return std::clamp<Common>(*res, inf, sup);
}
template<std::integral T0, std::integral T1, std::integral Limit>
inline auto mul_clamp(const T0 x, const T1 y, const Limit inf, const Limit sup) noexcept(NO_EXCEPT) {
using Common = std::common_type_t<T0, T1, Limit>;
const auto res = mul_overflow<Common>(x, y);
if(!res) {
if((x > 0) xor (y > 0)) return inf;
else return sup;
assert(false);
}
return std::clamp<Common>(*res, inf, sup);
}
template<class T>
inline constexpr T sqrt_floor(const T x) noexcept(NO_EXCEPT) {
return static_cast<T>(std::sqrt(static_cast<long double>(x)));
}
template<class T>
inline constexpr T sqrt_ceil(const T x) noexcept(NO_EXCEPT) {
T res = sqrt_floor(x);
if constexpr(std::is_floating_point_v<T>) {
while(res * res < x) res += 1;
}
else {
while(mul_overflow(res, res).value_or(std::numeric_limits<T>::max()) < x) ++res;
}
return res;
}
template<class T, std::integral K>
inline constexpr T kth_root_floor(T x, const K k) noexcept(NO_EXCEPT) {
assert(x >= 0);
if(std::signed_integral<K>) assert(k > 0);
if(x <= 1 or k == 1) return x;
constexpr auto DIGITS = std::numeric_limits<T>::digits;
if(k >= DIGITS) return T{1};
if(k == 2) return sqrt_floor(x);
constexpr auto MAX = std::numeric_limits<T>::max();
if(x == MAX) --x;
auto pow = [&](T t, i64 p) {
if(p == 0) return T{1};
T res = 1;
while(p) {
if(p & 1) {
res = mul_overflow(res, t).value_or(MAX);
}
t = mul_overflow(t, t).value_or(MAX);
p >>= 1;
}
return res;
};
auto res = static_cast<T>(std::pow(x, std::nextafter(1 / static_cast<double>(k), 0)));
while(pow(res + 1, k) <= x) ++res;
return res;
}
template<std::integral T>
T inline constexpr extended_gcd(const T& a, const T& b, T& x, T& y) noexcept {
if(b == 0) {
x = 1;
y = 0;
return a;
}
const T d = extended_gcd(b, a%b, y, x);
y -= a / b * x;
return d;
};
template<std::integral T>
std::pair<T, spair<T>> inline constexpr extended_gcd(const T& a, const T& b) noexcept {
T x, y;
const T d = extended_gcd(a, b, x, y);
return { d, spair<T>{ x, y } };
};
template<std::integral T>
std::optional<spair<T>> inline constexpr bezout_equation(const T& a, const T& b, const T& c) noexcept {
if(a == 0) {
if(b == 0) {
if(c == 0) return spair<T>{ 0, 0 };
else { };
}
if(c % b == 0) return spair<T>{ 0, c / b };
return {};
}
if(b == 0) {
const auto ans = bezout_equation(b, a, c);
if(ans.has_value()) return swapped(ans.value());
return {};
}
T x, y;
const T gcd = extended_gcd(a, b, x, y);
if(c % gcd != 0) return {};
const T p = c / gcd;
return spair<T>{ x * p, y * p };
};
} // namespace uni
#line 16 "utility/functional.hpp"
#line 18 "utility/functional.hpp"
namespace uni {
namespace internal {
template<class T> constexpr T plus(const T a, const T b) noexcept(NO_EXCEPT) { return std::plus<T>{}(a, b); }
template<class T> constexpr T minus(const T a, const T b) noexcept(NO_EXCEPT) { return std::minus<T>{}(a, b); }
template<class T> constexpr T bit_xor(const T a, const T b) noexcept(NO_EXCEPT) { return a xor b; }
} // namespace internal
template<class T, class U> inline auto to_optional_if_equal(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v == ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_over(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v > ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_or_over(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v >= ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_under(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v < ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline auto to_optional_if_or_under(const T& v, const U& ill) noexcept(NO_EXCEPT) -> std::optional<T> {
return v <= ill ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class F> inline auto to_optional_if(const T& v, F&& f) noexcept(NO_EXCEPT) -> decltype(f(v), std::optional<T>{}){
return f(v) ? std::optional<T>{} : std::optional<T>(v);
}
template<class T, class U> inline bool chmin(T &a, const U& b) noexcept(NO_EXCEPT) { return (a>b ? a=b, true : false); }
template<class T, class U> inline bool chmax(T &a, const U& b) noexcept(NO_EXCEPT) { return (a<b ? a=b, true : false); }
template<class T, class... Ts> inline bool chmin(T &a, Ts... b) noexcept(NO_EXCEPT) { return chmin(a, min(b...)); }
template<class T, class... Ts> inline bool chmax(T &a, Ts... b) noexcept(NO_EXCEPT) { return chmax(a, max(b...)); }
template<class... Ts>
inline constexpr std::common_type_t<Ts...> tuple_sum(const std::tuple<Ts...>& tuple, const std::common_type_t<Ts...>& base = std::common_type_t<Ts...>()) noexcept(NO_EXCEPT) {
std::common_type_t<Ts...> res = base;
tuple_for_each(tuple, [&](const auto& v) constexpr { res += v; });
return res;
}
template<class... Ts>
inline constexpr std::common_type_t<Ts...> min_element(const std::tuple<Ts...>& tuple) noexcept(NO_EXCEPT) {
return std::apply([&](auto&&... v) constexpr { return min(v...); }, tuple);
}
template<class... Ts>
inline constexpr std::common_type_t<Ts...> max_element(const std::tuple<Ts...>& tuple) noexcept(NO_EXCEPT) {;
return std::apply([&](auto&&... v) constexpr { return max(v...); }, tuple);
}
template<interval_notation INTERVAL, class T0, class T1, class T2>
inline constexpr bool in_range(const T0& x, const T1& l, const T2& r) noexcept(NO_EXCEPT) {
if constexpr(INTERVAL == interval_notation::right_open) return l <= x and x < r;
else if constexpr(INTERVAL == interval_notation::left_open) return l < x and x <= r;
else if constexpr(INTERVAL == interval_notation::open) return l < x and x < r;
return l <= x and x <= r;
}
template<class F, class Tuple>
constexpr void tuple_for_each(F&& f, Tuple&& tuple) {
std::apply(
[&]<class... Ts>(Ts&&... elems) {
(std::invoke(f, std::forward<Ts>(elems)), ...);
},
std::forward<Tuple>(tuple)
);
}
template<class F, class Tuple>
constexpr auto tuple_transform(F&& f, Tuple&& tuple) {
return std::apply(
[&]<class...Ts>(Ts&&... elems) {
return internal::tuple_or_pair_t<std::invoke_result_t<F&,Ts>...>(
std::invoke(f, std::forward<Ts>(elems))...
);
},
std::forward<Tuple>(tuple)
);
}
} // namespace uni
#line 20 "adaptor/internal/input.hpp"
#line 2 "numeric/modular/modint_interface.hpp"
#line 6 "numeric/modular/modint_interface.hpp"
#line 9 "numeric/modular/modint_interface.hpp"
#line 11 "numeric/modular/modint_interface.hpp"
#line 2 "numeric/modular/builtin_reduction.hpp"
#line 5 "numeric/modular/builtin_reduction.hpp"
#line 8 "numeric/modular/builtin_reduction.hpp"
#line 10 "numeric/modular/builtin_reduction.hpp"
#line 12 "numeric/modular/builtin_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct builtin_reduction {
using value_type = Value;
using large_type = Large;
private:
value_type _mod;
public:
static constexpr int digits = std::numeric_limits<value_type>::digits;
static constexpr value_type max() noexcept { return std::numeric_limits<value_type>::max(); }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
constexpr builtin_reduction() noexcept = default;
constexpr builtin_reduction(const value_type mod) noexcept(NO_EXCEPT) : _mod(mod) {
assert(0 < mod && mod < builtin_reduction::max());
}
inline constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) { return v % this->_mod; }
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x >= this->_mod - y) x -= this->_mod;
x += y;
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += this->_mod;
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const value_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 0) return 0;
return uni::pow(v, p, [this](const value_type x, const value_type y) { return this->multiply(x, y); });
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x <=> y;
}
constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) { return v; }
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
using common_type = std::common_type_t<T, value_type>;
const common_type mod = static_cast<common_type>(this->_mod);
if(std::is_constant_evaluated()) {
v %= mod;
if constexpr(std::signed_integral<T>) {
if(v < 0) v += mod;
}
}
else {
if(v > 0 && static_cast<common_type>(v) >= mod) {
v %= mod;
}
if constexpr(std::signed_integral<T>) {
if(v < 0) {
if(static_cast<common_type>(-v) <= mod) v += mod;
else {
v %= mod;
if(v != 0) v += mod;
}
}
}
}
return static_cast<value_type>(v);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) { return this->_mod == 1 ? 0 : v; }
};
} // namespace internal
using builtin_reduction_32bit = internal::builtin_reduction<u32, u64>;
using builtin_reduction_64bit = internal::builtin_reduction<u64, u128>;
} // namespace uni
#line 2 "numeric/modular/binary_reduction.hpp"
#line 7 "numeric/modular/binary_reduction.hpp"
#line 10 "numeric/modular/binary_reduction.hpp"
#line 13 "numeric/modular/binary_reduction.hpp"
#line 2 "numeric/bit.hpp"
#include <immintrin.h>
#line 13 "numeric/bit.hpp"
#line 16 "numeric/bit.hpp"
#line 18 "numeric/bit.hpp"
namespace uni {
template<std::unsigned_integral T>
constexpr T multiply_high(const T x, const T y) noexcept(NO_EXCEPT) {
constexpr int digits = std::numeric_limits<T>::digits;
if constexpr(digits <= 16) {
return static_cast<T>((static_cast<u32>(x) * static_cast<u32>(y)) >> digits);
}
else if constexpr(digits <= 32) {
return static_cast<T>((static_cast<u64>(x) * static_cast<u64>(y)) >> digits);
}
else if constexpr(digits <= 64) {
return static_cast<T>((static_cast<u128>(x) * static_cast<u128>(y)) >> digits);
}
else {
constexpr int h_digits = digits / 2;
constexpr T mask = (T{ 1 } << h_digits) - 1;
const T xh = x >> h_digits, yh = y >> h_digits;
const T xl = x & mask, yl = y & mask;
const T ph = xh * yh, pl = xl * yl;
return (((pl >> h_digits) + (xh + xl) * (yh + yl) - (ph + pl)) >> h_digits) + ph;
}
}
template<std::unsigned_integral T>
inline constexpr int highest_bit_pos(const T v) noexcept(NO_EXCEPT) {
return (int)std::bit_width(v) - 1; // cast to int for GCC12
}
template<std::unsigned_integral T>
inline constexpr int lowest_bit_pos(const T v) noexcept(NO_EXCEPT) {
if(v == 0) return -1;
return std::countr_zero(v);
}
template<std::unsigned_integral T, std::integral I = int>
__attribute__((target("bmi2")))
inline constexpr T clear_higher_bits(const T v, const I p) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
constexpr int DIGITS = std::numeric_limits<T>::digits;
assert(p <= DIGITS);
if constexpr(DIGITS <= 32) return _bzhi_u32(v, static_cast<u32>(p));
if constexpr(DIGITS <= 64) return _bzhi_u64(v, static_cast<u64>(p));
else {
static_assert(DIGITS <= 128);
constexpr std::uint64_t MAX64 = std::numeric_limits<std::uint64_t>::max();
const std::uint64_t high = v >> 64;
const std::uint64_t low = v & MAX64;
if(p < 64) return _bzhi_u64(low, p);
return low | (T{_bzhi_u64(high, p - 64)} << 64);
}
}
template<std::unsigned_integral T, std::integral I = int> constexpr T shiftl(const T, const I = 1);
template<std::unsigned_integral T, std::integral I = int> constexpr T shiftr(const T, const I = 1);
template<std::unsigned_integral T, std::integral I>
constexpr T shiftl(const T x, const I n) {
constexpr int DIGITS = std::numeric_limits<T>::digits;
if constexpr(std::signed_integral<I>) {
if(n < 0) return shiftr(x, -n);
}
if(n >= DIGITS) return 0;
return x << n;
}
template<std::unsigned_integral T, std::integral I>
constexpr T shiftr(const T x, const I n) {
constexpr int DIGITS = std::numeric_limits<T>::digits;
if constexpr(std::signed_integral<I>) {
if(n < 0) return shiftl(x, -n);
}
if(n >= DIGITS) return 0;
return x >> n;
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr bool bit(const T x, const I p) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
assert(p < std::numeric_limits<T>::digits);
return shiftr(x, p) & T{1};
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr auto reset_bit(const T x, const I p) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
assert(p < std::numeric_limits<T>::digits);
return x & ~(T{1} << p);
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr auto set_bit(const T x, const I p, const bool bit = true) {
if constexpr(std::signed_integral<I>) assert(0 <= p);
assert(p < std::numeric_limits<T>::digits);
if(!bit) return reset_bit(x, p);
return x | (T{1} << p);
}
template<std::unsigned_integral T, std::integral I = int>
inline constexpr T lower_bits(const T x, const I digits) {
if constexpr(std::signed_integral<I>) assert(0 <= digits);
assert(digits <= std::numeric_limits<T>::digits);
return x & (uni::shiftl(x, digits) - 1);
}
// Thanks to: https://noshi91.github.io/Library/other/select64.cpp
constexpr int select64(const u64 x0, u32 k) {
const u64 x1 = (x0 & UINT64_C(0x5555555555555555)) + (x0 >> 1 & UINT64_C(0x5555555555555555));
const u64 x2 = (x1 & UINT64_C(0x3333333333333333)) + (x1 >> 2 & UINT64_C(0x3333333333333333));
const u64 x3 = (x2 & UINT64_C(0x0F0F0F0F0F0F0F0F)) + (x2 >> 4 & UINT64_C(0x0F0F0F0F0F0F0F0F));
const u64 x4 = (x3 & UINT64_C(0x00FF00FF00FF00FF)) + (x3 >> 8 & UINT64_C(0x00FF00FF00FF00FF));
const u64 x5 = (x4 & UINT64_C(0x0000FFFF0000FFFF)) + (x4 >> 16 & UINT64_C(0x0000FFFF0000FFFF));
int res = 0;
u32 t;
t = x5 & 0xFFFFFFFF;
if(t <= k) k -= t, res += 32;
t = x4 >> res & 0xFFFF;
if(t <= k) k -= t, res += 16;
t = x3 >> res & 0xFF;
if(t <= k) k -= t, res += 8;
t = x2 >> res & 0xF;
if(t <= k) k -= t, res += 4;
t = x1 >> res & 0x3;
if(t <= k) k -= t, res += 2;
t = x0 >> res & 0x1;
if(t <= k) k -= t, res += 1;
return res;
}
namespace internal {
template<std::unsigned_integral T>
constexpr T binary_gcd(T a, T b) noexcept(NO_EXCEPT) {
if(!a || !b) return a | b;
T t, s = std::countr_zero(a | b);
a >>= std::countr_zero(a);
do {
b >>= std::countr_zero(b);
if(a > b) t = a, a = b, b = t;
b -= a;
} while(b);
return a << s;
}
template<std::signed_integral T>
inline constexpr T binary_gcd(const T a, const T b) noexcept(NO_EXCEPT) {
return binary_gcd(a < 0 ? -a : a, b < 0 ? -b : b);
}
} // namespace internal
template<std::integral T0, std::integral T1>
inline constexpr auto binary_gcd(T0 v0, T1 v1) noexcept(NO_EXCEPT) {
using common_type = std::common_type_t<T0, T1>;
return internal::binary_gcd(static_cast<common_type>(v0), static_cast<common_type>(v1));
}
template<std::unsigned_integral T, std::unsigned_integral S>
inline constexpr bool is_subset_of(T target, S superset) noexcept(NO_EXCEPT) {
return (target & ~superset) == 0;
}
template<std::unsigned_integral T, std::unsigned_integral S>
inline constexpr bool is_superset_of(T target, S subset) noexcept(NO_EXCEPT) {
return (~target & subset) == 0;
}
template<std::unsigned_integral S0, std::unsigned_integral S1>
inline constexpr auto comapre_as_bitset(S0 s0, S1 s1) noexcept(NO_EXCEPT) {
if(s0 == s1) return std::partial_ordering::equivalent;
if(is_subset_of(s0, s1)) return std::partial_ordering::less;
if(is_superset_of(s0, s1)) return std::partial_ordering::greater;
return std::partial_ordering::unordered;
}
} // namespace uni
#line 16 "numeric/modular/binary_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value>
struct binary_reduction {
using value_type = Value;
private:
value_type _mask;
public:
static constexpr int digits = std::numeric_limits<value_type>::digits;
static constexpr value_type max() noexcept { return std::numeric_limits<value_type>::max(); }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mask + 1; }
constexpr binary_reduction() noexcept = default;
constexpr explicit inline binary_reduction(const value_type mod) noexcept(NO_EXCEPT) : _mask(mod - 1) {
assert(std::has_single_bit(mod));
}
inline constexpr value_type reduce(const value_type v) const noexcept(NO_EXCEPT) { return v; }
inline constexpr value_type add(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x + y;
}
inline constexpr value_type subtract(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x - y;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x * y;
}
template<std::integral K>
inline constexpr value_type pow(const value_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mask == 0) return 0;
return uni::pow(v, p);
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->revert(x) <=> this->revert(y);
}
constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
return v;
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
return static_cast<value_type>(v);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return v & this->_mask;
}
};
} // namespace internal
using binary_reduction_32bit = internal::binary_reduction<u32>;
using binary_reduction_64bit = internal::binary_reduction<u64>;
using binary_reduction_128bit = internal::binary_reduction<u128>;
} // namespace uni
#line 2 "numeric/modular/barrett_reduction.hpp"
#line 8 "numeric/modular/barrett_reduction.hpp"
#line 11 "numeric/modular/barrett_reduction.hpp"
#line 14 "numeric/modular/barrett_reduction.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL_JUDGE
#define DEBUGGER_ENABLED
#define DEBUGGER_COLORED_OUTPUT 1
#endif
#line 2 "debugger/debug.hpp"
#line 9 "debugger/debug.hpp"
#include <array>
#line 13 "debugger/debug.hpp"
#include <bitset>
#include <deque>
#include <queue>
#include <stack>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#line 22 "debugger/debug.hpp"
#include <iomanip>
#line 26 "debugger/debug.hpp"
#line 2 "numeric/int128.hpp"
#include <cctype>
#line 9 "numeric/int128.hpp"
#line 12 "numeric/int128.hpp"
#line 14 "numeric/int128.hpp"
namespace std {
template<class C, class S>
auto& operator>>(std::basic_istream<C, S>& in, uni::i128& v) noexcept(NO_EXCEPT) {
std::string str; in >> str;
v = 0;
bool negative = (str[0] == '-');
REP(d, std::ranges::next(str.begin(), negative), str.end()) {
assert(std::isdigit(*d));
v = v * 10 + *d - '0';
}
if(negative) v *= -1;
return in;
}
template<class C, class S>
auto& operator>>(std::basic_istream<C, S>& in, uni::u128& v) noexcept(NO_EXCEPT) {
std::string str; in >> str;
v = 0U;
assert(str[0] != '-');
REP(d, str.begin(), str.end()) {
assert(std::isdigit(*d));
v = v * 10U + *d - '0';
}
return in;
}
template<class C, class S>
auto& operator<<(std::basic_ostream<C, S>& out, uni::i128 v) noexcept(NO_EXCEPT) {
if(v == 0) return out << 0;
if(v < 0) out << '-', v *= -1;
std::string str;
while(v > 0) str += static_cast<char>(v%10) + '0', v /= 10;
std::reverse(str.begin(), str.end());
return out << str;
}
template<class C, class S>
auto& operator<<(std::basic_ostream<C, S>& out, uni::u128 v) noexcept(NO_EXCEPT) {
if(v == 0) return out << 0U;
std::string str;
while(v > 0) str += static_cast<char>(v%10U) + '0', v /= 10U;
std::reverse(str.begin(), str.end());
return out << str;
}
}
#line 29 "debugger/debug.hpp"
#line 34 "debugger/debug.hpp"
#include <typeinfo>
#include <cxxabi.h>
namespace debugger {
template<class T>
auto _debug (T&& val) -> decltype(val._debug()) {
return val._debug();
}
std::ostream *cdebug = &std::clog;
#ifdef DEBUGGER_COLORED_OUTPUT
constexpr std::string COLOR_LINE = "\033[3;35m";
constexpr std::string COLOR_IDENTIFIER = "\033[32m";
constexpr std::string COLOR_INIT = "\033[m";
constexpr std::string COLOR_STRING = "\033[33m";
constexpr std::string COLOR_TYPE = "\033[34m";
constexpr std::string COLOR_NUMERIC = "\033[36m";
constexpr std::string COLOR_LITERAL_OPERATOR = "\033[31m";
#else
constexpr std::string COLOR_LINE = "";
constexpr std::string COLOR_IDENTIFIER = "";
constexpr std::string COLOR_INIT = "";
constexpr std::string COLOR_STRING = "";
constexpr std::string COLOR_TYPE = "";
constexpr std::string COLOR_NUMERIC = "";
constexpr std::string COLOR_LITERAL_OPERATOR = "";
#endif
using Brackets = std::pair<std::string, std::string>;
template<class T>
std::string dump(T&&);
template<class T>
const std::string get_type_name(T&& val) {
const char* const name = typeid(std::forward<T>(val)).name();
int status = -4;
char* const demangled_name = abi::__cxa_demangle(name, NULL, NULL, &status);
std::string res{name};
if (status == 0) {
res = std::string(demangled_name);
free(demangled_name);
}
return COLOR_TYPE + res + COLOR_INIT;
}
struct debug_t : std::string {
using std::string::string;
debug_t(const std::string& str) {
this->assign(str);
}
};
template<size_t N, class T>
void dump_tuple_impl([[maybe_unused]] T&& val, std::stringstream &res) {
if constexpr(N < std::tuple_size_v<std::remove_cvref_t<T>>) {
res << dump(std::get<N>(val));
if constexpr(N < std::tuple_size_v<std::remove_cvref_t<T>> - 1) res << ", ";
dump_tuple_impl<N + 1>(std::forward<T>(val), res);
}
}
template<std::ranges::input_range R>
std::string dump_range_impl(R&& range, const Brackets& brcs = { "[", "]" }, const std::string& spl = ", ") {
std::stringstream res;
res << brcs.first << " ";
auto itr = std::ranges::begin(range);
auto end = std::ranges::end(std::forward<R>(range));
while(itr != end) {
if(std::ranges::next(itr) == end) res << dump(*itr) << " ";
else res << dump(*itr) << spl;
++itr;
}
res << brcs.second ;
return res.str();
}
std::string dump_debug_t(debug_t info) {
return info;
}
struct dump_primitive_like {
std::string operator()(std::nullptr_t) const {
return COLOR_INIT;
}
template<uni::internal::pointer T>
std::string operator()(const T ptr) const {
return dump(*ptr);
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::basic_string>
std::string operator()(T&& val) const {
std::stringstream res;
res << COLOR_STRING << "`" << val << "`" << COLOR_INIT;
return res.str();
}
std::string operator()(const char val) const {
std::stringstream res;
res << COLOR_STRING << "\'" << val << "\'" << COLOR_INIT;
return res.str();
}
std::string operator()(const char val[]) const {
std::stringstream res;
res << COLOR_STRING << "\"" << val << "\"" << COLOR_INIT;
return res.str();
}
std::string operator()(const unsigned char val) const {
std::stringstream res;
res << COLOR_NUMERIC << static_cast<int>(val) << COLOR_INIT;
return res.str();
}
std::string operator()(const bool val) const {
std::stringstream res;
res << COLOR_NUMERIC << (val ? "true" : "false" ) << COLOR_INIT;
return res.str();
}
template<uni::internal::arithmetic T>
std::string operator()(const T val) const {
std::stringstream res;
res << std::setprecision(std::numeric_limits<T>::digits10) << val;
auto str = res.str();
std::string dst = "";
while(str.length() > 3) {
dst = ',' + str.substr(str.length() - 3, 3) + dst;
str = str.substr(0, str.length() - 3);
}
return COLOR_NUMERIC + str + dst + COLOR_LITERAL_OPERATOR + uni::internal::literal_operator_v<T> + COLOR_INIT;
};
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::optional>
std::string operator()(T&& val) const {
if(val.has_value()) return dump(*val);
return COLOR_TYPE + "invalid" + COLOR_INIT;
}
};
struct dump_bitset {
template<std::size_t N>
std::string operator()(const std::bitset<N>& val) const {
std::stringstream res;
res << COLOR_NUMERIC << val.to_string() << COLOR_INIT;
return res.str();
}
};
struct dump_has_val {
template<class T>
requires requires (T val) { val.val(); }
std::string operator()(T&& val) const {
return dump(val.val());
}
};
struct dump_iterator {
template<std::input_or_output_iterator I>
std::string operator()(I&& itr) const {
return COLOR_TYPE + "<iterator> " + COLOR_INIT+ dump(*itr);
}
};
struct dump_wrapper {
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::map>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::multimap>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_map>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_multimap>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::set>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::multiset>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_set>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::unordered_multiset>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("{", "}"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::valarray>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("[", "]"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::vector>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("[", "]"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::deque>
std::string operator()(T&& val) const {
return dump_range_impl(val, Brackets("[", "]"));
}
template<uni::internal::derived_from_template<std::queue> T>
std::string operator()(T val) const {
std::vector<typename T::value_type> vec;
while(!val.empty()) vec.emplace_back(val.front()), val.pop();
return dump_range_impl(vec, Brackets("<", ">"));
}
template<uni::internal::derived_from_template<std::stack> T>
std::string operator()(T val) const {
std::vector<typename T::value_type> vec;
while(!val.empty()) vec.emplace_back(val.top()), val.pop();
std::ranges::reverse(vec);
return dump_range_impl(vec, Brackets("<", ">"));
}
template<uni::internal::derived_from_template<std::priority_queue> T>
std::string operator()(T val) const {
std::vector<typename T::value_type> vec;
while(!val.empty()) vec.emplace_back(val.top()), val.pop();
return dump_range_impl(vec, Brackets("<", ">"));
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::pair>
std::string operator()(T&& val) const {
std::stringstream res;
res << "( " << dump(val.first) << ", " << dump(val.second) << " )";
return res.str();
}
template<class T>
requires uni::internal::derived_from_template<std::remove_cvref_t<T>, std::tuple>
std::string operator()(T&& val) const {
std::stringstream res;
res << "( ";
dump_tuple_impl<0>(val, res);
res << " )";
return res.str();
}
};
struct dump_range {
template<std::ranges::input_range T>
std::string operator()(T&& val) const {
return dump_range_impl(val);
}
};
struct dump_loggable {
template<uni::internal::loggable T>
std::string operator()(T&& val) const {
auto res = _debug(val);
if constexpr(std::same_as<decltype(res), debug_t>) {
return res;
}
else {
return dump(res);
}
}
};
template<class T>
std::string dump(T&& val) {
if constexpr(std::same_as<std::remove_cvref_t<T>, debug_t>) {
// return "debug_t";
return dump_debug_t(std::forward<T>(val));
}
if constexpr(std::invocable<dump_primitive_like, T>) {
// return "primitive";
return dump_primitive_like{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_loggable, T>) {
// return "loggable";
return dump_loggable{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_has_val, T>) {
// return "has val";
return dump_has_val{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_bitset, T>) {
// return "bitset";
return dump_bitset{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_iterator, T>) {
// return "iterator";
return dump_iterator{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_wrapper, T>) {
// return "wrapper";
return dump_wrapper{}(std::forward<T>(val));
}
if constexpr(std::invocable<dump_range, T>) {;
// return "range";
return dump_range{}(std::forward<T>(val));
}
return "== dump error ==";
}
template<class T> void debug(T&& val, const std::string& endl) {
*cdebug << dump(val) << endl << std::flush;
}
constexpr std::string_view WHITESPACES = " \n\r\t\f\v";
std::string ltrim(const std::string &s)
{
size_t start = s.find_first_not_of(WHITESPACES);
return (start == std::string::npos) ? "" : s.substr(start);
}
std::string rtrim(const std::string &s)
{
size_t end = s.find_last_not_of(WHITESPACES);
return (end == std::string::npos) ? "" : s.substr(0, end + 1);
}
std::string trim(const std::string &s) {
return rtrim(ltrim(s));
}
std::vector<std::string> split(const std::string& str) {
static constexpr char SEPARATOR = ',';
static constexpr char ESCAPE = '\\';
static constexpr std::string_view QUOTATIONS = "\"\'";
static constexpr std::string_view PARENTHESES = "()[]{}<>";
static constexpr auto PARENTHESES_KINDS = std::ranges::size(PARENTHESES);
static_assert(PARENTHESES_KINDS % 2 == 0);
std::vector<std::string> res = { "" };
bool quoted = false;
std::array<int,(PARENTHESES_KINDS / 2)> enclosed = { 0 };
for(auto itr = std::ranges::begin(str); itr != std::ranges::end(str); ++itr) {
if(std::ranges::find(QUOTATIONS, *itr) != std::ranges::end(QUOTATIONS)) {
if(itr == std::ranges::begin(str) or *std::ranges::prev(itr) != ESCAPE) {
quoted ^= true;
}
}
if(const auto found = std::ranges::find(PARENTHESES, *itr); found != std::ranges::end(PARENTHESES)) {
if(not quoted) {
auto& target = enclosed[std::ranges::distance(std::begin(PARENTHESES), found) / 2];
target = std::max(0, target - static_cast<int>((std::ranges::distance(std::begin(PARENTHESES), found) % 2) * 2) + 1);
}
}
if(
not quoted
and static_cast<std::size_t>(std::ranges::count(enclosed, 0)) == std::ranges::size(enclosed)
and *itr == SEPARATOR
) {
res.push_back("");
}
else {
res.back() += *itr;
}
}
for(auto&& v : res) v = trim(v);
return res;
}
template<class Arg> void raw(std::nullptr_t, Arg&& arg) { *cdebug << std::forward<Arg>(arg) << std::flush; }
template<class Arg> void raw(Arg&& arg) { *cdebug << dump(std::forward<Arg>(arg)) << std::flush; }
void debug(const std::vector<std::string>, const size_t, const int, const std::string) { debug(nullptr, COLOR_INIT + "\n"); }
std::map<std::pair<std::string, int>, int> count;
template<class Head, class... Tail>
void debug(
const std::vector<std::string> args, const size_t idx,
const int line, const std::string path,
Head&& H, Tail&&... T
) {
if(idx == 0) {
std::string file = path.substr(path.find_last_of("/") + 1);
debug(nullptr, COLOR_LINE + file + " #" + std::to_string(line) + " (" + std::to_string(count[{ file, line }]++) + ")" + COLOR_INIT);
}
debug(nullptr, "\n - ");
const std::string content = dump(H);
const std::string type_name = get_type_name(std::forward<Head>(H));
debug(nullptr, COLOR_IDENTIFIER + args[idx] + COLOR_INIT + " : ");
debug(nullptr, content);
if(type_name.size() + content.size() >= 300) debug(nullptr, "\n ");
debug(nullptr, " " + type_name);
debug(args, idx + 1, 0, path, std::forward<Tail>(T)...);
}
} // namespace debugger
#line 13 "template/debug.hpp"
#ifdef DEBUGGER_ENABLED
#define debug(...) debugger::debug(debugger::split(#__VA_ARGS__), 0, __LINE__, __FILE__, __VA_ARGS__)
#define debug_(...) do { const std::string file = __FILE__; debugger::raw(nullptr, debugger::COLOR_LINE + file.substr(file.find_last_of("/") + 1) + " #" + std::to_string(__LINE__) + debugger::COLOR_INIT + " "); debugger::raw(__VA_ARGS__); debugger::raw(nullptr, debugger::COLOR_INIT + "\n"); } while(0);
#define DEBUG if constexpr(true)
#else
#define debug(...) ({ ; })
#define debug_(...) ({ ; })
#define DEBUG if constexpr(false)
#endif
#line 18 "numeric/modular/barrett_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct barrett_reduction {
using value_type = Value;
using large_type = Large;
private:
large_type _mod = 0, _mi;
inline constexpr std::pair<large_type,value_type> _reduce(const large_type v) const noexcept(NO_EXCEPT) {
large_type x = multiply_high(v, this->_mi);
return { x, static_cast<value_type>(v - x * this->_mod) };
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 1;
static constexpr value_type max() noexcept { return (value_type{ 1 } << barrett_reduction::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
constexpr barrett_reduction() noexcept = default;
constexpr explicit inline barrett_reduction(const value_type mod)
: _mod(mod), _mi(std::numeric_limits<large_type>::max() / mod + 1)
{
assert(0 < mod && mod <= barrett_reduction::max());
}
inline constexpr large_type quotient(const large_type v) const noexcept(NO_EXCEPT) {
const auto [ x, r ] = this->_reduce(v);
return static_cast<large_type>(this->_mod <= r ? x - 1 : x);
}
inline constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
const auto [ x, r ] = this->_reduce(v);
return static_cast<value_type>(this->_mod <= r ? r + this->_mod : r);
}
inline constexpr std::pair<large_type,value_type> divide(const large_type v) const noexcept(NO_EXCEPT) {
const auto [ x, r ] = this->_reduce(v);
if(this->_mod <= r) return { static_cast<large_type>(x - 1), static_cast<value_type>(r + this->_mod) };
return { static_cast<large_type>(x), static_cast<value_type>(r) };
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= this->_mod) x -= this->_mod;
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += this->_mod;
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
this->reduce(v), p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); }
);
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return x <=> y;
}
constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) { return v; }
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
using common_type = std::common_type_t<T, value_type>;
const common_type mod = static_cast<common_type>(this->_mod);
if(v > 0 && static_cast<common_type>(v) >= mod) {
if(static_cast<common_type>(v) <= barrett_reduction::max()) v = this->reduce(v);
else v %= mod;
}
if constexpr(std::signed_integral<T>) {
if(v < 0) {
if(static_cast<common_type>(-v) <= mod) v += mod;
else if(static_cast<common_type>(-v) <= barrett_reduction::max()) {
v = mod - this->reduce(static_cast<value_type>(-v - 1)) - 1;
}
else {
v %= mod;
if(v != 0) v += mod;
}
}
}
return static_cast<value_type>(v);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) { return this->reduce(v); }
};
} // namespace internal
using barrett_reduction_32bit = internal::barrett_reduction<u32, u64>;
using barrett_reduction_64bit = internal::barrett_reduction<u64, u128>;
} // namespace uni
#line 2 "numeric/modular/montgomery_reduction.hpp"
#line 7 "numeric/modular/montgomery_reduction.hpp"
#line 10 "numeric/modular/montgomery_reduction.hpp"
#line 16 "numeric/modular/montgomery_reduction.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct montgomery_reduction {
using value_type = Value;
using large_type = Large;
private:
value_type _mod = 0, _r2, _mp;
constexpr value_type _inv() const noexcept(NO_EXCEPT) {
value_type res = this->_mod;
while(this->_mod * res != 1) res *= value_type{ 2 } - this->_mod * res;
return res;
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 2;
static constexpr value_type max() noexcept { return (value_type{ 1 } << montgomery_reduction::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
value_type zero = 0;
value_type one;
constexpr montgomery_reduction() noexcept = default;
constexpr montgomery_reduction(const value_type mod) noexcept(NO_EXCEPT)
: _mod(mod), _r2(static_cast<value_type>(-static_cast<large_type>(mod) % mod)),
_mp(-this->_inv()), one(this->reduce(this->_r2))
{
assert((mod & 1) == 1);
assert(mod <= montgomery_reduction::max());
}
constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
return
static_cast<value_type>(
(
v + static_cast<large_type>(static_cast<value_type>(v) * this->_mp) * this->_mod
) >> std::numeric_limits<value_type>::digits
);
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= (this->_mod << 1)) x -= (this->_mod << 1);
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += (this->_mod << 1);
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
v, p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); },
static_cast<large_type>(this->one)
);
}
inline constexpr value_type normalize(const value_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < (this->_mod << 1));
if(v < this->_mod) return v;
return v - this->_mod;
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->normalize(x) <=> this->normalize(y);
}
inline constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
return this->multiply(v, this->_r2);
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
using common_type = std::common_type_t<T, value_type>;
const common_type mod2 = static_cast<common_type>(this->_mod << 1);
if(v > 0 && static_cast<common_type>(v) >= mod2) {
v %= mod2;
}
if constexpr(std::is_signed_v<T>) {
if(v < 0 && static_cast<common_type>(-v) >= mod2) {
v %= mod2;
if(v != 0) v += mod2;
}
}
return this->multiply(v, this->_r2);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return this->normalize(this->reduce(v));
}
};
// Thanks to: https://www.mathenachia.blog/even-mod-montgomery-impl/
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct arbitrary_montgomery_reduction {
using value_type = Value;
using large_type = Large;
private:
using context = arbitrary_montgomery_reduction;
static constexpr int width = std::numeric_limits<value_type>::digits;
value_type _mod = 0;
int _tz;
value_type _m0;
large_type _m0i, _mask;
value_type _r2;
constexpr large_type _inv() const noexcept(NO_EXCEPT) {
large_type res = this->_m0;
while(((this->_m0 * res) & this->_mask) != 1) res *= large_type{ 2 } - this->_m0 * res;
return res & this->_mask;
}
constexpr value_type _m0ip() const noexcept(NO_EXCEPT) {
if(this->_tz == 0) return 0;
value_type res = this->_m0;
const value_type mask = (value_type{ 1 } << this->_tz) - 1;
while(((this->_m0 * res) & mask) != 1) res *= value_type{ 2 } - this->_m0 * res;
return res & mask;
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 2;
static constexpr value_type max() noexcept { return (value_type{ 1 } << context::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
value_type one;
constexpr arbitrary_montgomery_reduction() noexcept = default;
constexpr arbitrary_montgomery_reduction(value_type m) noexcept(NO_EXCEPT) {
assert(0 < m);
if(this->_mod == m) return;
this->_mod = m;
this->_tz = std::countr_zero(m);
this->_m0 = m >> this->_tz;
assert(this->_mod < context::max());
this->_mask = (large_type{ 1 } << (context::width + this->_tz)) - 1;
this->_m0i = this->_inv();
{
const value_type x = (std::numeric_limits<large_type>::max() % this->_m0) + 1;
const value_type mask = (value_type{ 1 } << this->_tz) - 1;
this->_r2 = (x + ((((large_type{ 1 } - x) * this->_m0ip()) & mask) * this->_m0));
}
this->one = this->reduce(this->_r2);
}
constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
const value_type res =
static_cast<value_type>(
(
v +
this->_m0 *
((((v << std::numeric_limits<value_type>::digits) - v) * this->_m0i) & this->_mask)
) >> std::numeric_limits<value_type>::digits
);
return res;
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= (this->_mod << 1)) x -= (this->_mod << 1);
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += (this->_mod << 1);
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
v, p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); },
static_cast<large_type>(this->one)
);
}
inline constexpr value_type normalize(const value_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < (this->_mod << 1));
if(v < this->_mod) return v;
return v - this->_mod;
}
inline constexpr auto compare(const large_type x, const large_type y) const noexcept(NO_EXCEPT) {
return this->normalize(x) <=> this->normalize(y);
}
inline constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
return this->multiply(v, this->_r2);
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
using common_type = std::common_type_t<T, value_type>;
const common_type mod2 = static_cast<common_type>(this->_mod << 1);
if(v > 0 && static_cast<common_type>(v) >= mod2) {
v %= mod2;
}
if constexpr(std::signed_integral<T>) {
if(v < 0) {
if(static_cast<common_type>(-v) >= mod2) v %= mod2;
if(v < 0) v += mod2;
}
}
return this->multiply(v, this->_r2);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return this->normalize(this->reduce(v));
}
};
} // namespace internal
using montgomery_reduction_32bit = internal::montgomery_reduction<u32, u64>;
using montgomery_reduction_64bit = internal::montgomery_reduction<u64, u128>;
using arbitrary_montgomery_reduction_32bit = internal::arbitrary_montgomery_reduction<u32, u64>;
using arbitrary_montgomery_reduction_64bit = internal::arbitrary_montgomery_reduction<u64, u128>;
} // namespace uni
#line 16 "numeric/modular/modint_interface.hpp"
namespace uni {
namespace internal {
template<class T>
concept modint_family =
numeric<T> &&
has_static_one<T> && has_static_zero<T> &&
requires (T v, i64 p, typename T::value_type x) {
{ v.pow(p) } -> std::same_as<T>;
{ v.inv() } -> std::same_as<T>;
{ T::raw(x) } -> std::same_as<T>;
{ v.val() } -> std::same_as<typename T::value_type>;
{ T::mod() } -> std::same_as<typename T::value_type>;
{ T::max() } -> std::same_as<typename T::value_type>;
T::digits;
T::context::dynamic;
};
template<class T>
concept dynamic_modint_family =
modint_family<T> &&
T::context::dynamic &&
requires (typename T::value_type v) {
T::set_mod(v);
};
template<class T>
concept static_modint_family =
modint_family<T> &&
(!T::context::dynamic); //&&
// requires {
// T::is_prime;
// };
template<class T>
concept modular_reduction =
std::default_initializable<T> &&
std::constructible_from<T, typename T::value_type> &&
requires (T v, typename T::value_type x, i64 p) {
typename T::value_type;
T::digits;
{ T::max() } -> std::same_as<typename T::value_type>;
{ v.mod() } -> std::same_as<typename T::value_type>;
{ v.reduce(x) } -> std::same_as<typename T::value_type>;
{ v.add(x, x) } -> std::same_as<typename T::value_type>;
{ v.subtract(x, x) } -> std::same_as<typename T::value_type>;
{ v.multiply(x, x) } -> std::same_as<typename T::value_type>;
{ v.multiply(x, x) } -> std::same_as<typename T::value_type>;
{ v.pow(x, p) } -> std::same_as<typename T::value_type>;
{ v.convert_raw(x) } -> std::same_as<typename T::value_type>;
{ v.convert(x) } -> std::same_as<typename T::value_type>;
{ v.revert(x) } -> std::same_as<typename T::value_type>;
v.compare(x, x);
};
template<class T>
concept modular_context =
requires {
typename T::reductor;
typename T::value_type;
T::reduction;
};
} // namespace internal
template<internal::modular_reduction Reduction, typename Reduction::value_type Mod>
struct static_modular_context {
using reductor = Reduction;
using value_type = typename reductor::value_type;
static constexpr bool dynamic = false;
static constexpr reductor reduction = reductor(Mod);
private:
using context = static_modular_context;
};
template<internal::modular_reduction Reduction, i64 Id>
struct dynamic_modular_context {
using reductor = Reduction;
using value_type = typename reductor::value_type;
static constexpr bool dynamic = true;
static inline reductor reduction;
private:
using context = dynamic_modular_context;
public:
static constexpr void set_mod(const value_type mod) noexcept(NO_EXCEPT) { context::reduction = reductor(mod); }
};
template<internal::modular_context> struct modint;
template<u32 Mod> using static_builtin_modular_context_32bit = static_modular_context<builtin_reduction_32bit, Mod>;
template<u64 Mod> using static_builtin_modular_context_64bit = static_modular_context<builtin_reduction_64bit, Mod>;
template<u32 Mod> using static_barrett_modular_context_32bit = static_modular_context<barrett_reduction_32bit, Mod>;
template<u64 Mod> using static_barrett_modular_context_64bit = static_modular_context<barrett_reduction_64bit, Mod>;
template<u32 Mod> using static_montgomery_modular_context_32bit = static_modular_context<montgomery_reduction_32bit, Mod>;
template<u64 Mod> using static_montgomery_modular_context_64bit = static_modular_context<montgomery_reduction_64bit, Mod>;
template<u32 Mod> using static_arbitrary_montgomery_modular_context_32bit = static_modular_context<arbitrary_montgomery_reduction_32bit, Mod>;
template<u64 Mod> using static_arbitrary_montgomery_modular_context_64bit = static_modular_context<arbitrary_montgomery_reduction_64bit, Mod>;
template<u32 Mod> using static_binary_modular_context_32bit = static_modular_context<binary_reduction_32bit, Mod>;
template<u64 Mod> using static_binary_modular_context_64bit = static_modular_context<binary_reduction_64bit, Mod>;
template<u128 Mod> using static_binary_modular_context_128bit = static_modular_context<binary_reduction_128bit, Mod>;
template<u32 Mod> using static_builtin_modint_32bit = modint<static_builtin_modular_context_32bit<Mod>>;
template<u64 Mod> using static_builtin_modint_64bit = modint<static_builtin_modular_context_64bit<Mod>>;
template<u32 Mod> using static_barrett_modint_32bit = modint<static_barrett_modular_context_32bit<Mod>>;
template<u64 Mod> using static_barrett_modint_64bit = modint<static_barrett_modular_context_64bit<Mod>>;
template<u32 Mod> using static_montgomery_modint_32bit = modint<static_montgomery_modular_context_32bit<Mod>>;
template<u64 Mod> using static_montgomery_modint_64bit = modint<static_montgomery_modular_context_64bit<Mod>>;
template<u32 Mod> using static_arbitrary_montgomery_modint_32bit = modint<static_arbitrary_montgomery_modular_context_32bit<Mod>>;
template<u64 Mod> using static_arbitrary_montgomery_modint_64bit = modint<static_arbitrary_montgomery_modular_context_64bit<Mod>>;
template<u32 Mod> using static_binary_modint_32bit = modint<static_binary_modular_context_32bit<Mod>>;
template<u64 Mod> using static_binary_modint_64bit = modint<static_binary_modular_context_64bit<Mod>>;
template<u128 Mod> using static_binary_modint_128bit = modint<static_binary_modular_context_128bit<Mod>>;
template<i64 Id> using dynamic_builtin_modular_context_32bit = dynamic_modular_context<builtin_reduction_32bit, Id>;
template<i64 Id> using dynamic_builtin_modular_context_64bit = dynamic_modular_context<builtin_reduction_64bit, Id>;
template<i64 Id> using dynamic_barrett_modular_context_32bit = dynamic_modular_context<barrett_reduction_32bit, Id>;
template<i64 Id> using dynamic_barrett_modular_context_64bit = dynamic_modular_context<barrett_reduction_64bit, Id>;
template<i64 Id> using dynamic_montgomery_modular_context_32bit = dynamic_modular_context<montgomery_reduction_32bit, Id>;
template<i64 Id> using dynamic_montgomery_modular_context_64bit = dynamic_modular_context<montgomery_reduction_64bit, Id>;
template<i64 Id> using dynamic_arbitrary_montgomery_modular_context_32bit = dynamic_modular_context<arbitrary_montgomery_reduction_32bit, Id>;
template<i64 Id> using dynamic_arbitrary_montgomery_modular_context_64bit = dynamic_modular_context<arbitrary_montgomery_reduction_64bit, Id>;
template<i64 Id> using dynamic_binary_modular_context_32bit = dynamic_modular_context<binary_reduction_32bit, Id>;
template<i64 Id> using dynamic_binary_modular_context_64bit = dynamic_modular_context<binary_reduction_64bit, Id>;
template<i64 Id> using dynamic_binary_modular_context_128bit = dynamic_modular_context<binary_reduction_128bit, Id>;
template<i64 Id> using dynamic_builtin_modint_32bit = modint<dynamic_builtin_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_builtin_modint_64bit = modint<dynamic_builtin_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_barrett_modint_32bit = modint<dynamic_barrett_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_barrett_modint_64bit = modint<dynamic_barrett_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_montgomery_modint_32bit = modint<dynamic_montgomery_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_montgomery_modint_64bit = modint<dynamic_montgomery_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_arbitrary_montgomery_modint_32bit = modint<dynamic_arbitrary_montgomery_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_arbitrary_montgomery_modint_64bit = modint<dynamic_arbitrary_montgomery_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_binary_modint_32bit = modint<dynamic_binary_modular_context_32bit<Id>>;
template<i64 Id> using dynamic_binary_modint_64bit = modint<dynamic_binary_modular_context_64bit<Id>>;
template<i64 Id> using dynamic_binary_modint_128bit = modint<dynamic_binary_modular_context_128bit<Id>>;
template<u32 Mod> using static_modint_32bit = static_builtin_modint_32bit<Mod>;
template<u64 Mod> using static_modint_64bit = static_builtin_modint_64bit<Mod>;
using modint998244353 = static_modint_32bit<998244353>;
using modint1000000007 = static_modint_32bit<1000000007>;
using modint_32 = dynamic_barrett_modint_32bit<-1>;
using modint_64 = dynamic_barrett_modint_64bit<-1>;
template<const unsigned Val, const unsigned Mod = 998244353>
const uni::static_modint_32bit<Mod> MINT = Val;
template<const unsigned Val, const unsigned Mod = 998244353>
const unsigned INV = uni::static_modint_32bit<Mod>{ Val }.inv().val();
template<const unsigned Val, const unsigned Mod = 998244353>
const int SINV = uni::static_modint_32bit<Mod>{ Val }.inv().val();
} // namespace uni
#line 22 "adaptor/internal/input.hpp"
#line 24 "adaptor/internal/input.hpp"
namespace uni {
template<std::derived_from<std::ios_base> Source = std::istream>
struct input_adaptor {
using source_type = Source;
private:
template<class T>
requires std::derived_from<T, std::valarray<typename T::value_type>>
auto _set(uni::internal::resolving_rank<6>, T& val) noexcept(NO_EXCEPT) -> int {
this->operator()(ALL(val));
return 0;
}
template<class T>
requires
requires (source_type& in, T& val) {
in >> val;
}
int _set(uni::internal::resolving_rank<5>, T& val) noexcept(NO_EXCEPT) {
*this->in >> val;
return 0;
}
template<std::ranges::range T>
int _set(uni::internal::resolving_rank<4>, T& val) noexcept(NO_EXCEPT) {
this->operator()(std::ranges::begin(val), std::ranges::end(val));
return 0;
}
template<class T>
requires
requires (T& val) {
val.first;
val.second;
}
int _set(uni::internal::resolving_rank<3>, T& val) noexcept(NO_EXCEPT) {
*this >> val.first >> val.second;
return 0;
}
template<class T>
requires
requires (T& val) {
std::get<0>(val);
}
int _set(uni::internal::resolving_rank<2>, T& val) noexcept(NO_EXCEPT) {
tuple_for_each([this](auto&& v) { *this >> v; }, val);
return 0;
}
template<uni::internal::modint_family T>
int _set(uni::internal::resolving_rank<1>, T& val) noexcept(NO_EXCEPT) {
std::int64_t v; std::cin >> v;
val = { v };
return 0;
}
template<class T>
requires
requires {
typename T::value_type;
}
int _set(uni::internal::resolving_rank<0>, T& val) noexcept(NO_EXCEPT) {
typename T::value_type v; *this >> v;
val = { v };
return 0;
}
protected:
template<class T>
source_type *set(T& val) noexcept(NO_EXCEPT) {
this->_set(uni::internal::resolving_rank<10>{}, val);
return this->in;
}
template<class T>
source_type *set(T&& _val) noexcept(NO_EXCEPT) {
T val = _val;
this->_set(uni::internal::resolving_rank<10>{}, val);
return this->in;
}
public:
using char_type = typename source_type::char_type;
source_type *in;
input_adaptor(source_type *_in = &std::cin) noexcept(NO_EXCEPT) : in(_in) {}
template<class T>
inline input_adaptor& operator>>(T&& s) noexcept(NO_EXCEPT) {
this->set(std::forward<T>(s));
return *this;
}
template<class T>
inline T one() noexcept(NO_EXCEPT) {
T val; *this >> val;
return val;
}
template<class T>
inline auto& operator()(T& val) noexcept(NO_EXCEPT) {
*this >> val;
return *this;
}
template<class T, class... Args>
inline auto& operator()(T& head, Args&... tail) noexcept(NO_EXCEPT) {
*this >> head;
this->operator()(tail...);
return *this;
}
template<std::input_or_output_iterator I, std::sentinel_for<I> S>
inline auto& operator()(I first, S last) noexcept(NO_EXCEPT) {
for(I itr=first; itr!=last; ++itr) *this >> *itr;
return *this;
}
explicit operator bool() const noexcept(NO_EXCEPT) { return (bool)*this->in; }
};
} // namespace uni
#line 2 "adaptor/internal/output.hpp"
#line 11 "adaptor/internal/output.hpp"
#line 15 "adaptor/internal/output.hpp"
namespace uni {
template<class Destination = std::ostream>
struct output_adaptor {
using destination_type = Destination;
private:
template<class T>
requires
requires (destination_type& out, T val) {
out << val;
}
int _put(uni::internal::resolving_rank<5>, T&& val) noexcept(NO_EXCEPT) {
*this->out << std::forward<T>(val);
return 0;
}
template<class T>
requires
requires (T&& val) {
val.val();
}
int _put(uni::internal::resolving_rank<4>, T&& val) noexcept(NO_EXCEPT) {
this->put(val.val());
return 0;
}
template<std::ranges::input_range T>
int _put(uni::internal::resolving_rank<3>, T&& val) noexcept(NO_EXCEPT) {
(*this)(std::ranges::begin(val), std::ranges::end(val), false);
return 0;
}
template<class T>
requires
requires (T&& val) {
val.first;
val.second;
}
int _put(uni::internal::resolving_rank<2>, T&& val) noexcept(NO_EXCEPT) {
*this << val.first, this->put_separator();
*this << val.second;
return 0;
}
template<class T>
requires
requires (T&& val) {
std::get<0>(val);
}
auto _put(uni::internal::resolving_rank<1>, T&& val) noexcept(NO_EXCEPT) {
std::apply([this](const auto&... args) constexpr { ((*this << args, this->put_separator()), ...); }, std::forward<T>(val));
return 0;
}
template<std::input_or_output_iterator T>
int _put(uni::internal::resolving_rank<0>, T&& val) noexcept(NO_EXCEPT) {
(*this)(*std::forward<T>(val));
return 0;
}
protected:
template<class T>
destination_type* put(T&& val) noexcept(NO_EXCEPT){
this->_put(uni::internal::resolving_rank<10>{}, std::forward<T>(val));
return this->out;
}
public:
using char_type = typename destination_type::char_type;
static constexpr auto sendl = std::endl<char_type,std::char_traits<char_type>>;
static constexpr auto sflush = std::flush<char_type,std::char_traits<char_type>>;
protected:
using sfunc_type = std::remove_const_t<decltype(output_adaptor::sendl)>;
public:
using separator_type = std::variant<std::string,sfunc_type>;
destination_type *out;
separator_type endline;
separator_type separator;
protected:
void put_separator() noexcept(NO_EXCEPT) {
if(this->separator.index() == 0) *this->out << std::get<std::string>(this->separator);
if(this->separator.index() == 1) *this->out << std::get<sfunc_type>(this->separator);
}
void put_endline() noexcept(NO_EXCEPT) {
if(this->endline.index() == 0) *this->out << std::get<std::string>(this->endline);
if(this->endline.index() == 1) *this->out << std::get<sfunc_type>(this->endline);
}
public:
template<class Terminator = std::string, class Separator = std::string>
output_adaptor(destination_type *des = &std::cout, Terminator endl = "\n", Separator sep = " ") noexcept(NO_EXCEPT)
: out(des), endline(endl), separator(sep)
{
*this << std::fixed << std::setprecision(20);
}
inline auto& seekp(const typename destination_type::off_type off, const std::ios_base::seekdir dir = std::ios_base::cur) noexcept(NO_EXCEPT) {
this->out->seekp(off, dir); return *this;
};
template<class T> inline output_adaptor& operator<<(T&& s) noexcept(NO_EXCEPT){
this->put(std::forward<T>(s));
return *this;
}
template<class T = std::string>
inline auto& operator()(T&& val = "") noexcept(NO_EXCEPT){
*this << std::forward<T>(val), this->put_endline();
return *this;
}
template<class T, class ...Args>
inline auto& operator()(T&& head, Args&& ...tail) noexcept(NO_EXCEPT){
*this << std::forward<T>(head), this->put_separator();
(*this)(std::forward<Args>(tail)...);
return *this;
}
template<std::forward_iterator I, std::sentinel_for<I> S>
inline auto& operator()(I first, S last, const bool terminate = true) noexcept(NO_EXCEPT) {
for(I itr=first; itr!=last;) {
*this << *itr;
if(++itr == last) {
if(terminate) this->put_endline();
}
else this->put_separator();
}
return *this;
}
template<class T>
inline auto& operator()(const std::initializer_list<T> vals) noexcept(NO_EXCEPT) {
std::vector wrapped(vals.begin(), vals.end());
(*this)(wrapped.begin(), wrapped.end());
return *this;
}
template<class T0, class T1>
inline auto& conditional(const bool cond, const T0& a, const T1& b) noexcept(NO_EXCEPT) {
if(cond) (*this)(a);
else (*this)(b);
return *this;
}
inline auto& yesno(const bool cond) noexcept(NO_EXCEPT) {
if(cond) this->yes();
else this->no();
return *this;
}
inline auto yes() noexcept(NO_EXCEPT) {
*this->out << "Yes";
this->put_endline();
return *this;
}
inline auto no() noexcept(NO_EXCEPT) {
*this->out << "No";
this->put_endline();
return *this;
}
inline auto flush() noexcept(NO_EXCEPT) {
*this->out << std::flush;
return *this;
}
};
} // namespace uni
#line 7 "adaptor/io.hpp"
namespace uni {
uni::input_adaptor _input;
uni::output_adaptor _print;
}
#define input uni::_input
#define print uni::_print
#line 2 "numeric/modular/modint.hpp"
#line 7 "numeric/modular/modint.hpp"
#line 10 "numeric/modular/modint.hpp"
#line 13 "numeric/modular/modint.hpp"
#line 15 "numeric/modular/modint.hpp"
#line 17 "numeric/modular/modint.hpp"
namespace uni {
namespace internal {
template<class, bool>
struct modint_base {};
template<class Mint>
struct modint_base<Mint, false> {
static constexpr Mint zero = Mint::_raw(0);
static constexpr Mint one = Mint::_one();
};
template<class Mint>
struct modint_base<Mint, true> {
static constexpr Mint zero = Mint::_raw(0);
static inline Mint one = Mint::_one();
};
} // internal
template<internal::modular_context Context>
struct modint : internal::modint_base<modint<Context>, Context::dynamic> {
using value_type = typename Context::value_type;
using context = Context;
private:
using base = internal::modint_base<modint, context::dynamic>;
friend base;
value_type _val = 0;
static constexpr auto _raw(const value_type v) noexcept(NO_EXCEPT) {
modint res;
res._val = v;
return res;
}
static constexpr auto _one() noexcept(NO_EXCEPT)
requires internal::has_static_one<typename modint::context::reductor>
{
return modint::_raw(modint::context::reduction.one);
}
static constexpr auto _one() noexcept(NO_EXCEPT)
requires (!internal::has_static_one<typename modint::context::reductor>)
{
return modint::_raw(1);
}
public:
static constexpr int digits = modint::context::reductor::digits;
static constexpr value_type max() noexcept { return modint::context::reductor::max(); }
static constexpr void set_mod(const value_type mod) noexcept(NO_EXCEPT)
requires requires(value_type mod) { modint::context::set_mod(mod); }
{
modint::context::set_mod(mod);
modint::one = modint::_one();
}
static constexpr auto mod() noexcept(NO_EXCEPT) { return modint::context::reduction.mod(); }
static constexpr auto raw(const value_type v) noexcept(NO_EXCEPT)
{
modint res;
res._val = modint::context::reduction.convert_raw(v);
return res;
};
constexpr modint() noexcept = default;
template<std::integral T>
constexpr modint(const T v) noexcept(NO_EXCEPT) : _val(modint::context::reduction.convert(v)) {}
inline constexpr auto val() const noexcept(NO_EXCEPT) {
return modint::context::reduction.revert(this->_val);
}
inline constexpr explicit operator value_type() const noexcept(NO_EXCEPT) { return this->_val; }
inline constexpr auto& operator+=(const modint& rhs) noexcept(NO_EXCEPT) {
this->_val = modint::context::reduction.add(this->_val, rhs._val);
return *this;
}
inline constexpr auto& operator-=(const modint& rhs) noexcept(NO_EXCEPT) {
this->_val = modint::context::reduction.subtract(this->_val, rhs._val);
return *this;
}
inline constexpr auto& operator*=(const modint& rhs) noexcept(NO_EXCEPT) {
this->_val = modint::context::reduction.multiply(this->_val, rhs._val);
return *this;
}
inline constexpr auto& operator/=(const modint& rhs) noexcept(NO_EXCEPT) { return *this *= rhs.inv(); }
template<std::integral K>
constexpr auto pow(const K n) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(n >= 0);
return modint::_raw(modint::context::reduction.pow(this->_val, n));
}
constexpr auto inv() const noexcept(NO_EXCEPT) {
using signed_value_type = std::make_signed_t<value_type>;
signed_value_type x = this->val(), y = modint::mod(), u = 1, v = 0;
while(y > 0) {
signed_value_type t = x / y;
std::swap(x -= t * y, y);
std::swap(u -= t * v, v);
}
assert(x == 1);
if(u < 0) u += v / x;
return modint::raw(u);
}
friend inline constexpr auto operator<=>(const modint& lhs, const modint& rhs) noexcept(NO_EXCEPT) {
return modint::context::reduction.compare(lhs._val, rhs._val);
}
friend inline constexpr bool operator==(const modint& lhs, const modint& rhs) noexcept(NO_EXCEPT) {
return lhs <=> rhs == 0;
}
inline constexpr auto& operator++() noexcept(NO_EXCEPT) { return *this += modint::one; }
inline constexpr auto& operator--() noexcept(NO_EXCEPT) { return *this -= modint::one; }
inline constexpr auto operator++(int) noexcept(NO_EXCEPT) { const modint res = *this; return ++*this, res; }
inline constexpr auto operator--(int) noexcept(NO_EXCEPT) { const modint res = *this; return --*this, res; }
inline constexpr auto operator+() const noexcept(NO_EXCEPT) { return *this; }
inline constexpr auto operator-() const noexcept(NO_EXCEPT) { return modint::zero - *this; }
friend inline constexpr auto operator+(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs += rhs; }
friend inline constexpr auto operator-(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs -= rhs; }
friend inline constexpr auto operator*(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs *= rhs; }
friend inline constexpr auto operator/(modint lhs, const modint& rhs) noexcept(NO_EXCEPT) { return lhs /= rhs; }
};
} // namespace uni
#line 2 "convolution/sum.hpp"
#line 7 "convolution/sum.hpp"
#line 2 "convolution/internal/butterfly.hpp"
#line 13 "convolution/internal/butterfly.hpp"
#line 16 "convolution/internal/butterfly.hpp"
#line 2 "numeric/internal/primitive_root.hpp"
#line 8 "numeric/internal/primitive_root.hpp"
#line 11 "numeric/internal/primitive_root.hpp"
#line 13 "numeric/internal/primitive_root.hpp"
#line 2 "numeric/internal/divisors.hpp"
#line 8 "numeric/internal/divisors.hpp"
#line 2 "numeric/internal/factorize.hpp"
#line 10 "numeric/internal/factorize.hpp"
#include <random>
#line 12 "numeric/internal/factorize.hpp"
#line 15 "numeric/internal/factorize.hpp"
#line 17 "numeric/internal/factorize.hpp"
#line 2 "numeric/internal/primality_test.hpp"
#line 7 "numeric/internal/primality_test.hpp"
#line 10 "numeric/internal/primality_test.hpp"
#line 13 "numeric/internal/primality_test.hpp"
namespace uni {
namespace internal {
//Thanks to: https://github.com/NyaanNyaan/library/blob/master/prime/fast-factorize.hpp
namespace fast_factorize_impl {
namespace internal {
// Miller-Rabin primality test
template<modint_family Mint>
constexpr bool primality_test(const u64 n, const std::vector<u64>& ws) noexcept(NO_EXCEPT) {
if constexpr(dynamic_modint_family<Mint>) Mint::set_mod(n);
assert(Mint::mod() == n);
const u64 d = (n - 1) >> std::countr_zero(n - 1);
const Mint rev = n - 1;
for(u64 w : ws) {
Mint x = w;
if(x == Mint::zero) continue;
x = x.pow(d);
if(x == Mint::one || x == rev) continue;
u64 t = d;
while(t != n - 1 && x != Mint::one && x != rev) x *= x, t <<= 1;
if(x != rev) return false;
}
return true;
}
// Thanks to: https://miller-rabin.appspot.com/
template<modint_family Small, modint_family Large = Small>
inline constexpr bool is_prime(const u64 n) noexcept(NO_EXCEPT) {
if(n == 0 || n == 1) return false;
if(~n & 1UL) return n == 2UL;
auto bases = [&]() constexpr noexcept(NO_EXCEPT) -> vector<u64> {
if(n < 341531UL) return { 9345883071009581737UL };
else if(n < 1050535501UL) return { 336781006125UL, 9639812373923155UL };
else if(n < 350269456337UL) return { 4230279247111683200UL, 14694767155120705706UL, 16641139526367750375UL };
else if(n < 55245642489451UL) return { 2UL, 141889084524735UL, 1199124725622454117UL, 11096072698276303650UL };
else if(n < 7999252175582851UL) return { 2UL, 4130806001517UL, 149795463772692060UL, 186635894390467037UL, 3967304179347715805UL };
else if(n < 585226005592931977UL) return { 2UL, 123635709730000UL, 9233062284813009UL, 43835965440333360UL, 761179012939631437UL, 1263739024124850375UL };
else return { 2UL, 325UL, 9375UL, 28178UL, 450775UL, 9780504UL, 1795265022UL };
};
if(n <= Small::max()) return primality_test<Small>(n, bases());
else return primality_test<Large>(n, bases());
}
} // namespace internal
} // namespace fast_factorize_impl
using fast_factorize_impl::internal::is_prime;
} // namespace internal
} // namespace uni
#line 21 "numeric/internal/factorize.hpp"
#line 2 "random/engine.hpp"
#line 7 "random/engine.hpp"
#line 9 "random/engine.hpp"
#line 12 "random/engine.hpp"
#line 14 "random/engine.hpp"
#line 2 "hash/general_hasher.hpp"
#line 7 "hash/general_hasher.hpp"
#line 11 "hash/general_hasher.hpp"
#line 13 "hash/general_hasher.hpp"
namespace uni {
template<std::unsigned_integral R, std::integral T>
constexpr R shrink(T x) noexcept(NO_EXCEPT) {
constexpr int DIGITS_R = std::numeric_limits<R>::digits;
constexpr int DIGITS_T = std::numeric_limits<R>::digits;
REPD(digits, DIGITS_R, DIGITS_T, DIGITS_R) {
x = (x >> digits) ^ uni::lower_bits(x, digits);
}
return x;
}
// Thanks to: https://gist.github.com/badboy/6267743
template<class T>
constexpr u32 hash32(T x) {
if constexpr(std::integral<T>) {
if constexpr(std::signed_integral<T>) return hash32(to_unsigned(x));
constexpr int DIGITS_T = std::numeric_limits<T>::digits;
if constexpr(DIGITS_T <= 32) {
auto h = static_cast<u32>(x);
h = ~h + (h << 15);
h ^= (h >> 12);
h += (h << 2);
h ^= (h >> 4);
h *= 2057;
h ^= (h >> 16);
return h;
}
else if constexpr(DIGITS_T <= 64) {
auto h = static_cast<u64>(x);
h = (~h) + (h << 18);
h ^= (h >> 31);
h *= 21;
h ^= (h >> 11);
h += (h << 6);
h ^= (h >> 22);
return static_cast<u32>(h);
}
else {
return hash32(hash64(x));
}
}
else {
return hash32(std::hash<T>{}(x));
}
}
template<class T>
constexpr u64 hash64(T x) {
if constexpr(std::integral<T>) {
if constexpr(std::signed_integral<T>) return hash64(to_unsigned(x));
constexpr int DIGITS_T = std::numeric_limits<T>::digits;
if constexpr(DIGITS_T <= 64) {
auto h = static_cast<u64>(x);
h = (~h) + (h << 21);
h ^= (h >> 24);
h *= 265;
h ^= (h >> 14);
h *= 21;
h ^= (h >> 28);
h += h << 31;
return h;
}
else {
return hash64(shrink<u64>(x));
}
}
else {
return hash64(std::hash<T>{}(x));
}
}
template<class T>
struct hash {
inline constexpr auto operator()(const T& key) const noexcept(NO_EXCEPT) {
return static_cast<std::size_t>(uni::hash64(key));
}
};
} // namespace uni
#line 16 "random/engine.hpp"
// Thanks to: https://prng.di.unimi.it/
namespace uni {
namespace internal {
template<class Derived, class ResultType>
struct random_engine {
using result_type = ResultType;
static constexpr result_type MIN = std::numeric_limits<result_type>::min();
static constexpr result_type MAX = std::numeric_limits<result_type>::max();
static constexpr result_type min() noexcept(NO_EXCEPT) { return MIN; }
static constexpr result_type max() noexcept(NO_EXCEPT) { return MAX; }
template<std::unsigned_integral T = result_type>
constexpr random_engine(const T _seed = 0) noexcept(NO_EXCEPT) {
static_cast<Derived*>(this)->seed(_seed);
};
inline constexpr result_type operator()() noexcept(NO_EXCEPT) {
return static_cast<Derived*>(this)->next();
}
};
const i64 INTERNAL_RANDOM_GENERATOR_ID = -(1UL << 60);
}; // namespace internal
constexpr float to_float(const std::uint32_t x) noexcept(NO_EXCEPT) {
return float(x >> 8) * 0x1.0p-24f;
}
constexpr double to_double(const std::uint64_t x) noexcept(NO_EXCEPT) {
return double(x >> 11) * 0x1.0p-53;
}
struct mulberry32 : internal::random_engine<mulberry32, std::uint32_t> {
using internal::random_engine<mulberry32, std::uint32_t>::random_engine;
private:
std::uint32_t _x;
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T x) noexcept(NO_EXCEPT) { this->_x = x; }
inline constexpr std::uint32_t next() noexcept(NO_EXCEPT) {
std::uint32_t z = (this->_x += 0x6D2B79F5U);
z = (z ^ (z >> 15)) * (z | 1U);
z ^= z + (z ^ (z >> 7)) * (z | 61U);
return static_cast<std::uint32_t>(z ^ (z >> 14));
}
};
struct splitmix64 : internal::random_engine<splitmix64, std::uint64_t> {
using internal::random_engine<splitmix64, std::uint64_t>::random_engine;
private:
std::uint64_t _x;
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T x) noexcept(NO_EXCEPT) { this->_x = x; }
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
std::uint64_t z = (this->_x += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
return z ^ (z >> 31);
}
};
// xoroshiro64**
struct xoroshiro64ss : internal::random_engine<xoroshiro64ss, std::uint32_t> {
using internal::random_engine<xoroshiro64ss, std::uint32_t>::random_engine;
private:
std::uint32_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
mulberry32 gen32(hash32(_seed));
this->s[0] = gen32();
this->s[1] = gen32();
}
inline constexpr std::uint32_t next() noexcept(NO_EXCEPT) {
const std::uint32_t s0 = this->s[0];
std::uint32_t s1 = this->s[1];
const std::uint32_t res = std::rotl(s0 * 0x9E3779BBU, 5) * 5;
s1 ^= s0;
this->s[0] = std::rotl(s0, 26) ^ s1 ^ (s1 << 9);
this->s[1] = std::rotl(s1, 13);
return res;
}
};
struct xoroshiro128ss : internal::random_engine<xoroshiro128ss, std::uint64_t> {
using internal::random_engine<xoroshiro128ss, std::uint64_t>::random_engine;
private:
std::uint64_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
splitmix64 gen64(hash32(_seed));
this->s[0] = gen64();
this->s[1] = gen64();
}
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
const uint64_t s0 = this->s[0];
uint64_t s1 = this->s[1];
const uint64_t res = std::rotl(s0 * 5, 7) * 9;
s1 ^= s0;
this->s[0] = std::rotl(s0, 24) ^ s1 ^ (s1 << 16);
this->s[1] = std::rotl(s1, 37);
return res;
}
};
struct xoroshiro128pp : internal::random_engine<xoroshiro128pp, std::uint64_t> {
using internal::random_engine<xoroshiro128pp, std::uint64_t>::random_engine;
private:
std::uint64_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
splitmix64 gen64(hash32(_seed));
this->s[0] = gen64();
this->s[1] = gen64();
}
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
const std::uint64_t s0 = this->s[0];
std::uint64_t s1 = this->s[1];
const std::uint64_t res = std::rotl(s0 + s1, 17) + s0;
s1 ^= s0;
this->s[0] = std::rotl(s0, 49) ^ s1 ^ (s1 << 21); // a, b
this->s[1] = std::rotl(s1, 28); // c
return res;
}
};
// xoroshiro128+
struct xoroshiro128p : internal::random_engine<xoroshiro128p, std::uint64_t> {
using internal::random_engine<xoroshiro128p, std::uint64_t>::random_engine;
private:
std::uint64_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
splitmix64 gen64(hash64(_seed));
this->s[0] = gen64();
this->s[1] = gen64();
}
inline constexpr std::uint64_t next() noexcept(NO_EXCEPT) {
const std::uint64_t s0 = this->s[0];
std::uint64_t s1 = this->s[1];
const std::uint64_t res = s0 + s1;
s1 ^= s0;
this->s[0] = std::rotl(s0, 24) ^ s1 ^ (s1 << 16);
this->s[1] = std::rotl(s1, 37);
return res;
}
};
struct xoroshiro64s : internal::random_engine<xoroshiro64s, std::uint32_t> {
using internal::random_engine<xoroshiro64s, std::uint32_t>::random_engine;
private:
std::uint32_t s[2];
public:
template<std::unsigned_integral T>
inline constexpr void seed(const T _seed) noexcept(NO_EXCEPT) {
mulberry32 gen32(hash32(_seed));
this->s[0] = gen32();
this->s[1] = gen32();
}
inline constexpr std::uint32_t next() noexcept(NO_EXCEPT) {
const std::uint32_t s0 = s[0];
std::uint32_t s1 = s[1];
const std::uint32_t res = s0 * 0x9E3779BB;
s1 ^= s0;
s[0] = std::rotl(s0, 26) ^ s1 ^ (s1 << 9);
s[1] = std::rotl(s1, 13);
return res;
}
};
using random_engine_32bit = xoroshiro64ss;
using random_engine_64bit = xoroshiro128pp;
using random_engine_float = xoroshiro64s;
using random_engine_double = xoroshiro128p;
random_engine_32bit randi32;
random_engine_64bit randi64;
float randf() {
static random_engine_float gen;
return to_float(gen());
}
double randd() {
static random_engine_double gen;
return to_double(gen());
}
} // namespace uni
#line 23 "numeric/internal/factorize.hpp"
namespace uni {
namespace internal {
//Thanks to: https://github.com/NyaanNyaan/library/blob/master/prime/fast-factorize.hpp
namespace fast_factorize_impl {
namespace internal {
// Pollard's rho algorithm
template<modint_family Mint, class T>
T find_factor(const T n) noexcept(NO_EXCEPT) {
if(~n & 1) return 2;
if(is_prime<Mint>(n)) return n;
assert(static_cast<u64>(Mint::mod()) == n);
Mint rr;
auto f = [&](const Mint& x) noexcept(NO_EXCEPT) { return x * x + rr; };
static random_engine_64bit rand(std::random_device{}());
auto rand_ = [&]() noexcept(NO_EXCEPT) { return rand() % (n - 2) + 2; };
while(true) {
Mint x, y, ys, q = Mint::one;
rr = rand_(), y = rand_();
T g = 1;
constexpr int m = 128;
for(int r = 1; g == 1; r <<= 1) {
x = y;
for(int i = 0; i < r; ++i) y = f(y);
for(int k = 0; g == 1 && k < r; k += m) {
ys = y;
for(int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
g = uni::binary_gcd(q.val(), n);
}
}
if(g == n) {
do {
g = uni::binary_gcd((x - (ys = f(ys))).val(), n);
} while(g == 1);
}
if(g != n) return g;
}
assert(false);
}
template<modint_family Small, modint_family Large, class R>
void factorize(const u64 n, R *const res) noexcept(NO_EXCEPT) {
if(n <= 1) return;
u64 p;
if constexpr(std::same_as<Small, Large>) p = find_factor<Small, typename Small::value_type>(n);
else {
if(n <= Small::max()) p = find_factor<Small, typename Small::value_type>(n);
else p = find_factor<Large, typename Large::value_type>(n);
}
if(p == static_cast<u64>(n)) {
res->emplace_back(p);
return;
}
factorize<Small, Large>(p, res);
factorize<Small, Large>(n / p, res);
}
} // namespace internal
} // namespace fast_factorize_impl
using fast_factorize_impl::internal::factorize;
} // namespace internal
} // namespace uni
#line 12 "numeric/internal/divisors.hpp"
namespace uni {
namespace internal {
//Thanks to: https://github.com/NyaanNyaan/library/blob/master/prime/fast-factorize.hpp
template<modint_family Small, modint_family Large, class R>
void divisors(const u64 n, R *const res) noexcept(NO_EXCEPT) {
if(n == 0) return;
std::vector<u64> facts; factorize<Small, Large>(n, &facts);
std::ranges::sort(facts);
std::vector<std::pair<u64, int>> v;
for(auto &p : facts) {
if(v.empty() || v.back().first != p) {
v.emplace_back(p, 1);
} else {
v.back().second++;
}
}
using value_type = std::ranges::range_value_t<R>;
const auto size = std::ranges::ssize(v);
auto f = [&](auto rc, int i, value_type x) noexcept(NO_EXCEPT) -> void {
if(i == size) {
res->push_back(x);
return;
}
for(int j = v[i].second; ; --j) {
rc(rc, i + 1, x);
if(j == 0) break;
x *= static_cast<value_type>(v[i].first);
}
};
f(f, 0, 1);
}
} // namespace internal
} // namespace uni
#line 16 "numeric/internal/primitive_root.hpp"
#line 18 "numeric/internal/primitive_root.hpp"
namespace uni {
namespace internal {
// Thanks to: https://37zigen.com/primitive-root/
template<modint_family Small, modint_family Large, modint_family Mint, std::unsigned_integral T>
T primitive_root(const T p) noexcept(NO_EXCEPT) {
std::vector<T> pows;
factorize<Small, Large>(p - 1, &pows);
{
std::ranges::sort(pows);
const auto rest = std::ranges::unique(pows);
pows.erase(ALL(rest));
}
ITRR(pow, pows) pow = (p - 1) / pow;
if constexpr(dynamic_modint_family<Mint>) Mint::set_mod(p);
assert(Mint::mod() == p);
static random_engine_64bit rand;
while(true) {
const Mint x = rand();
if(x == Mint::zero) continue;
bool ok = true;
ITR(pow, pows) {
if(x.pow(pow) == Mint::one) {
ok = false;
break;
}
}
if(ok) return x.val();
}
return 0;
}
// Thanks to: atcoder::internal::primitive_root_constexpr
template<static_modint_family Mint>
constexpr u32 primitive_root_constexpr(u32 m) {
assert(Mint::mod() == m);
u32 divs[20]{}; divs[0] = 2;
u32 cnt = 1;
u64 x = (m - 1) / 2;
while(x % 2 == 0) x /= 2;
for(u64 i = 3; i * i <= x; i += 2) {
if(x % i == 0) {
divs[cnt++] = i;
while(x % i == 0) x /= i;
}
}
if(x > 1) divs[cnt++] = x;
for(u32 g = 2; ; g++) {
bool ok = true;
REP(i, cnt) {
if(Mint{ g }.pow((m - 1) / divs[i]) == 1) {
ok = false;
break;
}
}
if(ok) return g;
}
}
template<modint_family Small, modint_family Large = Small, std::integral Res = u64, bool FORCE_RANDOM = false>
constexpr Res primitive_root(const u64 p) noexcept(NO_EXCEPT) {
if constexpr(!FORCE_RANDOM) {
if(p == 2) return 1;
if(p == 167772161) return 3;
if(p == 469762049) return 3;
if(p == 754974721) return 11;
if(p == 998244353) return 3;
if(p == (UINT64_C(1) << 61) - 1) return 37;
}
if(std::is_constant_evaluated()) {
if constexpr(static_modint_family<Small> && std::same_as<Small, Large> && Small::mod() < (1U << 31)) {
assert(p <= std::numeric_limits<u32>::max());
return primitive_root_constexpr<Small>(p);
}
assert(false);
}
else {
if(p <= Small::max()) return primitive_root<Small, Large, Small, typename Small::value_type>(p);
else return primitive_root<Small, Large, Large, typename Large::value_type>(p);
}
}
} // namespace internal
} // namespace uni
#line 19 "convolution/internal/butterfly.hpp"
#line 21 "convolution/internal/butterfly.hpp"
#line 23 "convolution/internal/butterfly.hpp"
namespace uni {
namespace internal {
// Thanks to: atocder/convolution
template<uni::internal::modint_family mint>
struct fft_info {
static constexpr mint g = primitive_root<mint>(mint::mod());
static constexpr auto rank2 = std::countr_zero(mint::mod() - 1);
std::array<mint, rank2 + 1> root;
std::array<mint, rank2 + 1> iroot;
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
consteval fft_info() {
this->root[rank2] = g.pow((mint::mod() - 1) >> this->rank2);
this->iroot[rank2] = this->root[this->rank2].inv();
REPD(i, rank2) {
this->root[i] = this->root[i + 1] * this->root[i + 1];
this->iroot[i] = this->iroot[i + 1] * this->iroot[i + 1];
}
{
mint prod = mint::one, iprod = mint::one;
REP(i, rank2 - 1) {
this->rate2[i] = this->root[i + 2] * prod;
this->irate2[i] = this->iroot[i + 2] * iprod;
prod *= this->iroot[i + 2];
iprod *= this->root[i + 2];
}
}
{
mint prod = mint::one, iprod = mint::one;
REP(i, rank2 - 2) {
this->rate3[i] = this->root[i + 3] * prod;
this->irate3[i] = this->iroot[i + 3] * iprod;
prod *= this->iroot[i + 3];
iprod *= this->root[i + 3];
}
}
}
};
} // namespace internal
template<std::ranges::sized_range R>
requires internal::static_modint_family<std::ranges::range_value_t<R>>
void butterfly(R& v1) {
using mint = std::ranges::range_value_t<R>;
const auto n = std::ranges::ssize(v1);
const auto h = to_signed(std::countr_zero(to_unsigned(n)));
static constexpr internal::fft_info<mint> info;
internal::size_t len = 0;
while(len < h) {
if(h - len == 1) {
const internal::size_t p = 1 << (h - len - 1);
mint rot = mint::one;
REP(s, 1 << len) {
const internal::size_t offset = s << (h - len);
REP(i, p) {
const auto l = v1[i + offset];
const auto r = v1[i + offset + p] * rot;
v1[i + offset] = l + r;
v1[i + offset + p] = l - r;
}
if(s + 1 != (1 << len)) {
rot *= info.rate2[std::countr_zero(~to_unsigned(s))];
}
}
++len;
}
else {
const internal::size_t p = 1 << (h - len - 2);
const mint imag = info.root[2];
mint rot = mint::one;
REP(s, 1 << len) {
const mint rot2 = rot * rot;
const mint rot3 = rot2 * rot;
const internal::size_t offset = s << (h - len);
REP(i, p) {
const auto mod2 = 1ULL * mint::mod() * mint::mod();
const auto a0 = 1ULL * v1[i + offset].val();
const auto a1 = 1ULL * v1[i + offset + p].val() * rot.val();
const auto a2 = 1ULL * v1[i + offset + 2 * p].val() * rot2.val();
const auto a3 = 1ULL * v1[i + offset + 3 * p].val() * rot3.val();
const auto a1na3imag = 1ULL * mint{ a1 + mod2 - a3 }.val() * imag.val();
const auto na2 = mod2 - a2;
v1[i + offset] = a0 + a2 + a1 + a3;
v1[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
v1[i + offset + 2 * p] = a0 + na2 + a1na3imag;
v1[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if(s + 1 != (1 << len)) rot *= info.rate3[std::countr_zero(~to_unsigned(s))];
}
len += 2;
}
}
}
template<std::ranges::sized_range R>
requires internal::static_modint_family<std::ranges::range_value_t<R>>
void butterfly_inv(R& v1) {
using mint = std::ranges::range_value_t<R>;
const auto n = std::ranges::ssize(v1);
const auto h = std::countr_zero(to_unsigned(n));
static constinit internal::fft_info<mint> info;
internal::size_t len = h;
while(len > 0) {
if(len == 1) {
const internal::size_t p = 1 << (h - len);
mint irot = mint::one;
REP(s, 1 << (len - 1)) {
const internal::size_t offset = s << (h - len + 1);
REP(i, p) {
const auto l = v1[i + offset];
const auto r = v1[i + offset + p];
v1[i + offset] = l + r;
v1[i + offset + p] = to_unsigned(mint::mod() + l.val() - r.val()) * irot.val();
}
if(s + 1 != (1 << (len - 1))) irot *= info.irate2[std::countr_zero(~to_unsigned(s))];
}
--len;
}
else {
const auto p = 1 << (h - len);
const mint iimag = info.iroot[2];
mint irot = mint::one;
REP(s, 1 << (len - 2)) {
const mint irot2 = irot * irot;
const mint irot3 = irot2 * irot;
const internal::size_t offset = s << (h - len + 2);
REP(i, p) {
const auto a0 = 1ULL * v1[i + offset + 0 * p].val();
const auto a1 = 1ULL * v1[i + offset + 1 * p].val();
const auto a2 = 1ULL * v1[i + offset + 2 * p].val();
const auto a3 = 1ULL * v1[i + offset + 3 * p].val();
const auto a2na3iimag = 1ULL * mint{ (mint::mod() + a2 - a3) * iimag.val() }.val();
v1[i + offset] = a0 + a1 + a2 + a3;
v1[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
v1[i + offset + 2 * p] = (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.val();
v1[i + offset + 3 * p] = (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.val();
}
if(s + 1 != (1 << (len - 2))) irot *= info.irate3[std::countr_zero(~to_unsigned(s))];
}
len -= 2;
}
}
}
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::same_as<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::static_modint_family<std::ranges::range_value_t<R0>>
Res convolution_naive(R0&& v0, R1&& v1) {
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
Res ans(n + m - 1);
if(n < m) {
REP(j, m) REP(i, n) ans[i + j] += v0[i] * v1[j];
}
else {
REP(i, n) REP(j, m) ans[i + j] += v0[i] * v1[j];
}
return ans;
}
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::same_as<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::static_modint_family<std::ranges::range_value_t<R0>> &&
internal::resizable_range<R0> && internal::resizable_range<R1> &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution_fft(R0 v0, R1 v1) {
using mint = std::ranges::range_value_t<R0>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
const auto z = to_signed(std::bit_ceil(to_unsigned(n + m - 1)));
v0.resize(z);
butterfly(v0);
v1.resize(z);
butterfly(v1);
REP(i, z) v0[i] *= v1[i];
butterfly_inv(v0);
v0.resize(n + m - 1);
const mint iz = mint{ z }.inv();
REP(i, n + m - 1) v0[i] *= iz;
if constexpr(std::convertible_to<R0, Res>) return v0;
else return Res(ALL(v0));
}
} // namespace uni
#line 10 "convolution/sum.hpp"
#line 12 "convolution/sum.hpp"
namespace uni {
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::same_as<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::static_modint_family<std::ranges::range_value_t<R0>> &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution(R0&& v0, R1&& v1) {
using mint = std::ranges::range_value_t<R0>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
if(!n || !m) return {};
const auto z = to_signed(std::bit_ceil(to_unsigned(n + m - 1)));
assert((mint::mod() - 1) % z == 0);
// if(uni::min(n, m) <= 60) return convolution_naive<Res>(v0, v1);
return convolution_fft<Res>(v0, v1);
}
template<
u32 Mod = 998244353,
class Res,
std::ranges::sized_range R0, std::ranges::sized_range R1
>
requires
std::convertible_to<std::ranges::range_value_t<R0>, static_modint_32bit<Mod>> &&
std::convertible_to<std::ranges::range_value_t<R1>, static_modint_32bit<Mod>> &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution(R0&& v0, R1&& v1) {
using mint = static_modint_32bit<Mod>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
if(!n || !m) return {};
const auto z = to_signed(std::bit_ceil(to_unsigned(n + m - 1)));
assert((mint::mod() - 1) % z == 0);
std::vector<mint> a2(n), b2(m);
REP(i, n) a2[i] = mint{ v0[i] };
REP(i, m) b2[i] = mint{ v1[i] };
const auto c1 = convolution(a2, b2);
Res c(n + m - 1);
REP(i, n + m - 1) c[i] = c1[i].val();
return c;
}
template<class Res, std::ranges::sized_range R0, std::ranges::sized_range R1>
requires
std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
std::integral<std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>> &&
(
std::integral<std::ranges::range_value_t<Res>> ||
internal::modint_family<std::ranges::range_value_t<Res>>
) &&
std::convertible_to<std::ranges::range_value_t<R0>, std::ranges::range_value_t<Res>>
Res convolution(R0&& v0, R1&& v1) {
using res_value_type = std::ranges::range_value_t<Res>;
const auto n = std::ranges::ssize(v0);
const auto m = std::ranges::ssize(v1);
if(!n || !m) return {};
static constexpr i64 MOD0 = 167772161;
static constexpr i64 MOD1 = 469762049;
static constexpr i64 MOD2 = 754974721;
static constexpr auto M0 = res_value_type{ MOD0 };
static constexpr auto M1 = res_value_type{ MOD1 };
static constexpr auto M2 = res_value_type{ MOD2 };
static constexpr auto M0M1 = M0 * M1;
static constexpr auto M0M2 = M0 * M2;
static constexpr auto M1M2 = M1 * M2;
static constexpr auto M0M1M2 = M0 * M1 * M2;
static constexpr u64 r0 = atcoder::internal::inv_gcd(MOD1 * MOD2, MOD0).second;
static constexpr u64 r1 = atcoder::internal::inv_gcd(MOD0 * MOD2, MOD1).second;
static constexpr u64 r2 = atcoder::internal::inv_gcd(MOD0 * MOD1, MOD2).second;
static constexpr i64 i01 = atcoder::internal::inv_gcd(MOD0, MOD1).second;
static constexpr i64 i02 = atcoder::internal::inv_gcd(MOD0, MOD2).second;
static constexpr i64 i12 = atcoder::internal::inv_gcd(MOD1, MOD2).second;
static constexpr i64 i02i12 = (i02 * i12) % MOD2;
static constexpr size_t MAX_AB_BIT = 24;
static_assert(MOD0 % (1ull << MAX_AB_BIT) == 1, "MOD0 isn't enough to support an array length of 2^24.");
static_assert(MOD1 % (1ull << MAX_AB_BIT) == 1, "MOD1 isn't enough to support an array length of 2^24.");
static_assert(MOD2 % (1ull << MAX_AB_BIT) == 1, "MOD2 isn't enough to support an array length of 2^24.");
assert(n + m - 1 <= (1 << MAX_AB_BIT));
const auto c0 = convolution<MOD0, std::remove_cvref_t<R0>>(v0, v1);
const auto c1 = convolution<MOD1, std::remove_cvref_t<R0>>(v0, v1);
const auto c2 = convolution<MOD2, std::remove_cvref_t<R0>>(v0, v1);
Res c(n + m - 1);
REP(i, n + m - 1) {
if constexpr(internal::modint_family<res_value_type>) {
const auto c01 = ((c1[i] + MOD1 - c0[i]) * i01) % MOD1;
const auto c012 = ((c2[i] + MOD2 - c0[i]) * i02i12 + (MOD2 - c01) * i12) % MOD2;
c[i] = c0[i] + c01 * M0 + c012 * M0M1;
}
else {
res_value_type x = 0;
x += (c0[i] * r0) % MOD0 * M1M2;
x += (c1[i] * r1) % MOD1 * M0M2;
x += (c2[i] * r2) % MOD2 * M0M1;
auto diff = c2[i] - uni::mod(to_signed(x), to_signed(MOD2));
if (diff < 0) diff += MOD2;
static constexpr res_value_type offset[5] = { 0, 0, M0M1M2, 2 * M0M1M2, 3 * M0M1M2 };
x -= offset[diff % 5];
c[i] = x;
}
}
return c;
}
template<std::ranges::range R0, std::ranges::range R1>
requires
std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
internal::modint_family<std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>>
auto convolution(R0&& v0, R1&& v1) {
using common_type = std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>;
return convolution<valarray<common_type>>(v0, v1);
}
template<u32 Mod = 998244353, std::ranges::range R0, std::ranges::range R1>
requires
std::common_with<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>> &&
std::integral<std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>> &&
(
std::numeric_limits<
std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>
>::digits <= 64
)
auto convolution(R0&& v0, R1&& v1) {
using common_type = std::common_type_t<std::ranges::range_value_t<R0>, std::ranges::range_value_t<R1>>;
return convolution<Mod, valarray<common_type>>(v0, v1);
}
} // namespace uni
#line 20 "verify/yosupo-judge/convolution_mod_1000000007/0000.test.cpp"
using mint = uni::modint1000000007;
signed main() {
uni::i32 n, m; input >> n >> m;
uni::vector<uni::u64> a(n), b(m); input >> a >> b;
print(uni::convolution<uni::vector<mint>>(a, b));
}
verify/yosupo-judge/convolution_mod_1000000007/0000.test.cpp