#include "math/rational.hpp"
#pragma once #include <cassert> #include <numeric> #include <vector> using namespace std; #include "../internal/internal-type-traits.hpp" #include "../math-fast/gcd.hpp" // T : 値, U : 比較用 template <typename T, typename U> struct RationalBase { using R = RationalBase; using Key = T; T x, y; RationalBase() : x(0), y(1) {} template <typename T1> RationalBase(const T1& _x) : RationalBase<T, U>(_x, T1{1}) {} template <typename T1, typename T2> RationalBase(const pair<T1, T2>& _p) : RationalBase<T, U>(_p.first, _p.second) {} template <typename T1, typename T2> RationalBase(const T1& _x, const T2& _y) : x(_x), y(_y) { assert(y != 0); if (y == -1) x = -x, y = -y; if (y != 1) { T g; if constexpr (internal::is_broadly_integral_v<T>) { if constexpr (sizeof(T) == 16) { g = binary_gcd128(x, y); } else { g = binary_gcd(x, y); } } else { g = gcd(x, y); } if (g != 0) x /= g, y /= g; if (y < 0) x = -x, y = -y; } } // y = 0 の代入も認める static R raw(T _x, T _y) { R r; r.x = _x, r.y = _y; return r; } friend R operator+(const R& l, const R& r) { if (l.y == r.y) return R{l.x + r.x, l.y}; return R{l.x * r.y + l.y * r.x, l.y * r.y}; } friend R operator-(const R& l, const R& r) { if (l.y == r.y) return R{l.x - r.x, l.y}; return R{l.x * r.y - l.y * r.x, l.y * r.y}; } friend R operator*(const R& l, const R& r) { return R{l.x * r.x, l.y * r.y}; } friend R operator/(const R& l, const R& r) { return R{l.x * r.y, l.y * r.x}; } R& operator+=(const R& r) { return (*this) = (*this) + r; } R& operator-=(const R& r) { return (*this) = (*this) - r; } R& operator*=(const R& r) { return (*this) = (*this) * r; } R& operator/=(const R& r) { return (*this) = (*this) / r; } R operator-() const { return raw(-x, y); } R inverse() const { assert(x != 0); R r = raw(y, x); if (r.y < 0) r.x = -r.x, r.y = -r.y; return r; } R pow(long long p) const { R res{1}, base{*this}; while (p) { if (p & 1) res *= base; base *= base; p >>= 1; } return res; } friend bool operator==(const R& l, const R& r) { return l.x == r.x && l.y == r.y; }; friend bool operator!=(const R& l, const R& r) { return l.x != r.x || l.y != r.y; }; friend bool operator<(const R& l, const R& r) { return U{l.x} * r.y < U{l.y} * r.x; }; friend bool operator<=(const R& l, const R& r) { return l < r || l == r; } friend bool operator>(const R& l, const R& r) { return U{l.x} * r.y > U{l.y} * r.x; }; friend bool operator>=(const R& l, const R& r) { return l > r || l == r; } friend ostream& operator<<(ostream& os, const R& r) { os << r.x; if (r.x != 0 && r.y != 1) os << "/" << r.y; return os; } // T にキャストされるので T が bigint の場合は to_ll も要る T to_mint(T mod) const { assert(mod != 0); T a = y, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return U((u % mod + mod) % mod) * x % mod; } }; using Rational = RationalBase<long long, __int128_t>;
#line 2 "math/rational.hpp" #include <cassert> #include <numeric> #include <vector> using namespace std; #line 2 "internal/internal-type-traits.hpp" #include <type_traits> using namespace std; namespace internal { template <typename T> using is_broadly_integral = typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>, true_type, false_type>::type; template <typename T> using is_broadly_signed = typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>, true_type, false_type>::type; template <typename T> using is_broadly_unsigned = typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template <typename T> \ constexpr bool x##_v = x<T>::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<typename T::var>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; #define ENABLE_HAS_VAR(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; } // namespace internal #line 2 "math-fast/gcd.hpp" #include <algorithm> using namespace std; namespace BinaryGCDImpl { using u64 = unsigned long long; using i8 = char; u64 binary_gcd(u64 a, u64 b) { if (a == 0 || b == 0) return a + b; i8 n = __builtin_ctzll(a); i8 m = __builtin_ctzll(b); a >>= n; b >>= m; n = min(n, m); while (a != b) { u64 d = a - b; i8 s = __builtin_ctzll(d); bool f = a > b; b = f ? b : a; a = (f ? d : -d) >> s; } return a << n; } using u128 = __uint128_t; // a > 0 int ctz128(u128 a) { u64 lo = a & u64(-1); return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64); } u128 binary_gcd128(u128 a, u128 b) { if (a == 0 || b == 0) return a + b; i8 n = ctz128(a); i8 m = ctz128(b); a >>= n; b >>= m; n = min(n, m); while (a != b) { u128 d = a - b; i8 s = ctz128(d); bool f = a > b; b = f ? b : a; a = (f ? d : -d) >> s; } return a << n; } } // namespace BinaryGCDImpl long long binary_gcd(long long a, long long b) { return BinaryGCDImpl::binary_gcd(abs(a), abs(b)); } __int128_t binary_gcd128(__int128_t a, __int128_t b) { if (a < 0) a = -a; if (b < 0) b = -b; return BinaryGCDImpl::binary_gcd128(a, b); } /** * @brief binary GCD */ #line 10 "math/rational.hpp" // T : 値, U : 比較用 template <typename T, typename U> struct RationalBase { using R = RationalBase; using Key = T; T x, y; RationalBase() : x(0), y(1) {} template <typename T1> RationalBase(const T1& _x) : RationalBase<T, U>(_x, T1{1}) {} template <typename T1, typename T2> RationalBase(const pair<T1, T2>& _p) : RationalBase<T, U>(_p.first, _p.second) {} template <typename T1, typename T2> RationalBase(const T1& _x, const T2& _y) : x(_x), y(_y) { assert(y != 0); if (y == -1) x = -x, y = -y; if (y != 1) { T g; if constexpr (internal::is_broadly_integral_v<T>) { if constexpr (sizeof(T) == 16) { g = binary_gcd128(x, y); } else { g = binary_gcd(x, y); } } else { g = gcd(x, y); } if (g != 0) x /= g, y /= g; if (y < 0) x = -x, y = -y; } } // y = 0 の代入も認める static R raw(T _x, T _y) { R r; r.x = _x, r.y = _y; return r; } friend R operator+(const R& l, const R& r) { if (l.y == r.y) return R{l.x + r.x, l.y}; return R{l.x * r.y + l.y * r.x, l.y * r.y}; } friend R operator-(const R& l, const R& r) { if (l.y == r.y) return R{l.x - r.x, l.y}; return R{l.x * r.y - l.y * r.x, l.y * r.y}; } friend R operator*(const R& l, const R& r) { return R{l.x * r.x, l.y * r.y}; } friend R operator/(const R& l, const R& r) { return R{l.x * r.y, l.y * r.x}; } R& operator+=(const R& r) { return (*this) = (*this) + r; } R& operator-=(const R& r) { return (*this) = (*this) - r; } R& operator*=(const R& r) { return (*this) = (*this) * r; } R& operator/=(const R& r) { return (*this) = (*this) / r; } R operator-() const { return raw(-x, y); } R inverse() const { assert(x != 0); R r = raw(y, x); if (r.y < 0) r.x = -r.x, r.y = -r.y; return r; } R pow(long long p) const { R res{1}, base{*this}; while (p) { if (p & 1) res *= base; base *= base; p >>= 1; } return res; } friend bool operator==(const R& l, const R& r) { return l.x == r.x && l.y == r.y; }; friend bool operator!=(const R& l, const R& r) { return l.x != r.x || l.y != r.y; }; friend bool operator<(const R& l, const R& r) { return U{l.x} * r.y < U{l.y} * r.x; }; friend bool operator<=(const R& l, const R& r) { return l < r || l == r; } friend bool operator>(const R& l, const R& r) { return U{l.x} * r.y > U{l.y} * r.x; }; friend bool operator>=(const R& l, const R& r) { return l > r || l == r; } friend ostream& operator<<(ostream& os, const R& r) { os << r.x; if (r.x != 0 && r.y != 1) os << "/" << r.y; return os; } // T にキャストされるので T が bigint の場合は to_ll も要る T to_mint(T mod) const { assert(mod != 0); T a = y, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return U((u % mod + mod) % mod) * x % mod; } }; using Rational = RationalBase<long long, __int128_t>;