#pragma once
#include "../../../nt/gl/gcd/lib.hpp"
#include "../../../util/traits/others/lib.hpp"
namespace tifa_libs {
template <int_c T>
struct rational {
T num, den;
CEXP rational(T numerator = T(0), T denominator = T(1)) NE : num{numerator}, den{denominator} {
if (assert(den != 0); num == 0) den = 1;
else {
const T g = (T)gcd(num, den);
if CEXP (num /= g, den /= g; std::is_signed_v<T>)
if (den < 0) num = -num, den = -den;
}
}
CEXP rational& operator+=(T x) NE {
num += x * den;
return *this;
}
CEXP rational& operator-=(T x) NE {
num -= x * den;
return *this;
}
CEXP rational& operator*=(T x) NE {
const T g = (T)gcd(x, den);
num *= x / g, den /= g;
return *this;
}
CEXP rational& operator/=(T x) NE {
assert(x);
const T g = (T)gcd(x, num);
if CEXP (num /= g, den *= x / g; std::is_signed_v<T>)
if (den < 0) num = -num, den = -den;
return *this;
}
CEXP rational& operator+=(rational CR x) NE {
T g = (T)gcd(den, x.den);
num = num * (x.den / g) + x.num * (den /= g);
g = (T)gcd(num, g);
num /= g, den *= x.den / g;
return *this;
}
CEXP rational& operator-=(rational CR x) NE {
T g = (T)gcd(den, x.den);
num = num * (x.den / g) - x.num * (den /= g);
g = (T)gcd(num, g);
num /= g, den *= x.den / g;
return *this;
}
CEXP rational& operator*=(rational CR x) NE {
const T g1 = (T)gcd(num, x.den), g2 = (T)gcd(x.num, den);
num = num / g1 * (x.num / g2);
den = den / g2 * (x.den / g1);
return *this;
}
CEXP rational& operator/=(rational CR x) NE {
const T g1 = (T)gcd(num, x.num), g2 = (T)gcd(den, x.den);
if CEXP (num = num / g1 * (x.den / g2), den = den / g2 * (x.num / g1); std::is_signed_v<T>)
if (den < 0) num = -num, den = -den;
return *this;
}
friend CEXP rational operator+(rational x, T y) NE { return x += y; }
friend CEXP rational operator-(rational x, T y) NE { return x -= y; }
friend CEXP rational operator*(rational x, T y) NE { return x *= y; }
friend CEXP rational operator/(rational x, T y) NE { return x /= y; }
friend CEXP rational operator+(rational x, rational CR y) NE { return x += y; }
friend CEXP rational operator-(rational x, rational CR y) NE { return x -= y; }
friend CEXP rational operator*(rational x, rational CR y) NE { return x *= y; }
friend CEXP rational operator/(rational x, rational CR y) NE { return x /= y; }
CEXP rational operator+() CNE { return *this; }
CEXP rational operator-() CNE { return rational(-num, den); }
CEXP rational& operator++() NE {
num += den;
return *this;
}
CEXP rational& operator--() NE {
num -= den;
return *this;
}
friend CEXP int operator<=>(rational CR x, rational CR y) NE {
const auto _ = (x - y).num;
retif_((_ < 0), -1, _ > 0);
}
friend CEXP bool operator==(rational CR x, rational CR y) NE { return x.num == y.num && x.den == y.den; }
friend auto& operator>>(istream_c auto& is, rational& x) NE { return is >> x.num >> x.den; }
friend auto& operator<<(ostream_c auto& os, rational CR x) NE { return os << x.num << ' ' << x.den; }
template <arithm_c U>
CEXP U convert_to() CNE { return U(num) / U(den); }
};
} // namespace tifa_libs
#line 2 "src/math/ds/rational/lib.hpp"
#line 2 "src/nt/gl/gcd/lib.hpp"
#line 2 "src/util/traits/math/lib.hpp"
// clang-format off
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/traits/math/lib.hpp"
namespace tifa_libs {
template <class T> concept char_c = std::same_as<T, char> || std::same_as<T, signed char> || std::same_as<T, unsigned char>;
#pragma GCC diagnostic ignored "-Wpedantic"
template <class T> concept s128_c = std::same_as<T, __int128_t> || std::same_as<T, __int128>;
template <class T> concept u128_c = std::same_as<T, __uint128_t> || std::same_as<T, unsigned __int128>;
template <class T> concept i128_c = s128_c<T> || u128_c<T>;
#pragma GCC diagnostic warning "-Wpedantic"
template <class T> concept imost64_c = std::integral<T> && sizeof(T) * __CHAR_BIT__ <= 64;
template <class T> concept smost64_c = imost64_c<T> && std::signed_integral<T>;
template <class T> concept umost64_c = imost64_c<T> && std::unsigned_integral<T>;
template <class T> concept int_c = i128_c<T> || imost64_c<T>;
template <class T> concept sint_c = s128_c<T> || smost64_c<T>;
template <class T> concept uint_c = u128_c<T> || umost64_c<T>;
template <class T> concept arithm_c = std::is_arithmetic_v<T> || int_c<T>;
template <class T> concept mint_c = requires(T x) { {x.mod()} -> uint_c; {x.val()} -> uint_c; };
template <class T> concept dft_c = requires(T x, std::vector<TPN T::data_t> v, u32 n) { {x.size()} -> std::same_as<u32>; x.bzr(n); x.dif(v, n); x.dit(v, n); };
template <class T> concept ntt_c = dft_c<T> && requires(T x) { T::max_size; T::G; };
template <class T> struct to_sint : std::make_signed<T> {};
template <> struct to_sint<u128> { using type = i128; };
template <> struct to_sint<i128> { using type = i128; };
template <class T> using to_sint_t = TPN to_sint<T>::type;
template <class T> struct to_uint : std::make_unsigned<T> {};
template <> struct to_uint<u128> { using type = u128; };
template <> struct to_uint<i128> { using type = u128; };
template <class T> using to_uint_t = TPN to_uint<T>::type;
template <arithm_c T> struct to_bigger : std::make_unsigned<T> {};
#define _(w,ww) template <> struct to_bigger<w> { using type = ww; }
#define _2(w,ww) _(i##w,i##ww); _(u##w,u##ww);
_2(8, 16); _2(16, 32); _2(32, 64); _2(64, 128); _(f32, f64); _(f64, f128);
#undef _2
#undef _
template <class T> using to_bigger_t = TPN to_bigger<T>::type;
template <arithm_c T> CEXP T inf_v = [] {
if CEXP(sint_c<T>) return T(to_uint_t<T>(-1) / 4 - 1);
else if CEXP(uint_c<T>) return T(-1) / 2 - 1;
else return std::numeric_limits<T>::max() / 2 - 1;
}();
} // namespace tifa_libs
// clang-format on
#line 4 "src/nt/gl/gcd/lib.hpp"
namespace tifa_libs {
namespace gcd_impl_ {
template <uint_c T, uint_c U>
CEXP std::common_type_t<T, U> gcd__(T u, U v) NE {
using W = std::common_type_t<T, U>;
retif_((!u || !v) [[unlikely]], u ^ v);
const auto k = std::__countr_zero(u | v);
u >>= k, v >>= k;
do {
if (W const _ = v >> std::__countr_zero(v); u > _) v = u - _, u = _;
else v = _ - u;
} while (v);
return u << k;
}
} // namespace gcd_impl_
template <int_c T, int_c U>
CEXP auto gcd(T a, U b) NE { return gcd_impl_::gcd__((to_uint_t<T>)abs(a), (to_uint_t<U>)abs(b)); }
} // namespace tifa_libs
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 5 "src/math/ds/rational/lib.hpp"
namespace tifa_libs {
template <int_c T>
struct rational {
T num, den;
CEXP rational(T numerator = T(0), T denominator = T(1)) NE : num{numerator}, den{denominator} {
if (assert(den != 0); num == 0) den = 1;
else {
const T g = (T)gcd(num, den);
if CEXP (num /= g, den /= g; std::is_signed_v<T>)
if (den < 0) num = -num, den = -den;
}
}
CEXP rational& operator+=(T x) NE {
num += x * den;
return *this;
}
CEXP rational& operator-=(T x) NE {
num -= x * den;
return *this;
}
CEXP rational& operator*=(T x) NE {
const T g = (T)gcd(x, den);
num *= x / g, den /= g;
return *this;
}
CEXP rational& operator/=(T x) NE {
assert(x);
const T g = (T)gcd(x, num);
if CEXP (num /= g, den *= x / g; std::is_signed_v<T>)
if (den < 0) num = -num, den = -den;
return *this;
}
CEXP rational& operator+=(rational CR x) NE {
T g = (T)gcd(den, x.den);
num = num * (x.den / g) + x.num * (den /= g);
g = (T)gcd(num, g);
num /= g, den *= x.den / g;
return *this;
}
CEXP rational& operator-=(rational CR x) NE {
T g = (T)gcd(den, x.den);
num = num * (x.den / g) - x.num * (den /= g);
g = (T)gcd(num, g);
num /= g, den *= x.den / g;
return *this;
}
CEXP rational& operator*=(rational CR x) NE {
const T g1 = (T)gcd(num, x.den), g2 = (T)gcd(x.num, den);
num = num / g1 * (x.num / g2);
den = den / g2 * (x.den / g1);
return *this;
}
CEXP rational& operator/=(rational CR x) NE {
const T g1 = (T)gcd(num, x.num), g2 = (T)gcd(den, x.den);
if CEXP (num = num / g1 * (x.den / g2), den = den / g2 * (x.num / g1); std::is_signed_v<T>)
if (den < 0) num = -num, den = -den;
return *this;
}
friend CEXP rational operator+(rational x, T y) NE { return x += y; }
friend CEXP rational operator-(rational x, T y) NE { return x -= y; }
friend CEXP rational operator*(rational x, T y) NE { return x *= y; }
friend CEXP rational operator/(rational x, T y) NE { return x /= y; }
friend CEXP rational operator+(rational x, rational CR y) NE { return x += y; }
friend CEXP rational operator-(rational x, rational CR y) NE { return x -= y; }
friend CEXP rational operator*(rational x, rational CR y) NE { return x *= y; }
friend CEXP rational operator/(rational x, rational CR y) NE { return x /= y; }
CEXP rational operator+() CNE { return *this; }
CEXP rational operator-() CNE { return rational(-num, den); }
CEXP rational& operator++() NE {
num += den;
return *this;
}
CEXP rational& operator--() NE {
num -= den;
return *this;
}
friend CEXP int operator<=>(rational CR x, rational CR y) NE {
const auto _ = (x - y).num;
retif_((_ < 0), -1, _ > 0);
}
friend CEXP bool operator==(rational CR x, rational CR y) NE { return x.num == y.num && x.den == y.den; }
friend auto& operator>>(istream_c auto& is, rational& x) NE { return is >> x.num >> x.den; }
friend auto& operator<<(ostream_c auto& os, rational CR x) NE { return os << x.num << ' ' << x.den; }
template <arithm_c U>
CEXP U convert_to() CNE { return U(num) / U(den); }
};
} // namespace tifa_libs
src/math/ds/rational/lib.hpp
src/math/frac_itv/lib.hpp