#line 2 "numeric/quotient_enumerator.hpp"
#include <cassert>
#include <tuple>
#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 "internal/iterator.hpp"
#include <utility>
#include <type_traits>
#include <iterator>
#include <variant>
#include <compare>
#include <ranges>
#line 13 "internal/iterator.hpp"
#line 2 "internal/types.hpp"
#include <cstdint>
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 2 "internal/type_traits.hpp"
#include <iostream>
#include <vector>
#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 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 10 "numeric/quotient_enumerator.hpp"
#line 2 "numeric/arithmetic.hpp"
#line 5 "numeric/arithmetic.hpp"
#include <cstring>
#line 7 "numeric/arithmetic.hpp"
#include <string>
#include <functional>
#line 10 "numeric/arithmetic.hpp"
#include <optional>
#line 12 "numeric/arithmetic.hpp"
#include <concepts>
#include <bit>
#include <atcoder/math>
#line 2 "snippet/aliases.hpp"
#line 8 "snippet/aliases.hpp"
#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/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/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 25 "numeric/arithmetic.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 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 "numeric/internal/mod.hpp"
#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 "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/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 12 "numeric/quotient_enumerator.hpp"
namespace uni {
template<class T, bool CEIL = false>
struct quotient_enumerator {
using value_type = std::tuple<T,T,T>; // (q, l, r)
using size_type = T;
private:
T _n = 0, _n_impl = 0;
size_type _size = -1;
protected:
using iterator_interface = internal::bidirectional_iterator_interface<const value_type>;
public:
// Enumerate tuple of (q, l, r), which means (floor/ceil)(_n/k) == q (l <= k <= r).
quotient_enumerator(const T n) noexcept(NO_EXCEPT) : _n(n), _n_impl(n - CEIL) { assert(n > 0); }
struct iterator;
using const_iterator = iterator;
inline auto begin() noexcept(NO_EXCEPT) { return iterator(this->_n_impl, 1); }
inline auto end() noexcept(NO_EXCEPT) { return iterator(this->_n_impl, this->_n + 1); }
inline auto rbegin() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->end()); }
inline auto rend() noexcept(NO_EXCEPT) { return std::make_reverse_iterator(this->begin()); }
inline auto size() noexcept(NO_EXCEPT) {
if(this->_size < 0) {
size_type r = uni::sqrt_floor(this->_n_impl);
this->_size = 2 * r - (this->_n_impl < r * (r + 1)) + CEIL;
}
return this->_size;
}
struct iterator : virtual iterator_interface {
using value_type = quotient_enumerator::value_type;
using reference = value_type;
protected:
T _n_impl = 0;
T _q = 0, _l = 0, _r = 0;
void _set_l(const T l) noexcept(NO_EXCEPT) {
this->_l = l, this->_q = this->_n_impl / l;
if(this->_q == 0) {
if(CEIL) {
if(l == this->_n_impl + 1) this->_r = l;
}
return;
}
this->_r = this->_n_impl / this->_q;
}
void _set_r(const T r) noexcept(NO_EXCEPT) {
this->_r = r, this->_q = this->_n_impl / r;
this->_l = this->_n_impl / (this->_q + 1) + 1;
}
public:
iterator() noexcept = default;
iterator(const T n, const T l) noexcept(NO_EXCEPT) : _n_impl(n) { this->_set_l(l); }
friend inline bool operator==(const iterator& lhs, const iterator& rhs) noexcept(NO_EXCEPT) { return lhs._l == rhs._l; }
inline value_type operator*() const noexcept(NO_EXCEPT) { return { this->_q + CEIL, this->_l, this->_r }; }
inline auto& operator++() noexcept(NO_EXCEPT) { this->_set_l(this->_r + 1); return *this; }
inline auto& operator--() noexcept(NO_EXCEPT) { this->_set_r(this->_l - 1); return *this; }
inline auto operator++(int) noexcept(NO_EXCEPT) { const auto res = *this; this->_set_l(this->_r + 1); return res; }
inline auto operator--(int) noexcept(NO_EXCEPT) { const auto res = *this; this->_set_r(this->_l - 1); return res; }
};
};
} // namespace uni
namespace std::ranges {
template<class T>
inline constexpr bool enable_borrowed_range<uni::quotient_enumerator<T>> = true;
} // namespace std::ranges
numeric/quotient_enumerator.hpp