#include "math/bigint-binary.hpp"
#include <algorithm> #include <cassert> #include <cmath> #include <iostream> #include <tuple> #include <utility> #include <vector> using namespace std; #include "../ntt/arbitrary-ntt.hpp" namespace BinaryBigIntImpl { using u32 = unsigned int; using u64 = unsigned long long; using i64 = long long; // 0 は neg=false, dat={} として扱う struct BinaryBigInt { using M = BinaryBigInt; bool neg; vector<u32> dat; BinaryBigInt() : neg(false), dat() {} BinaryBigInt(bool _neg, const vector<u32>& _dat) : neg(_neg), dat(_dat) {} BinaryBigInt(const string& S, int base) : neg(false) { assert(base == 16); int ie = -1; if (S[0] == '-') neg = true, ie++; for (int r = S.size() - 1; r > ie; r -= 8) { int l = max(r - 8, ie); u32 x = 0; for (int i = l + 1; i <= r; i++) { int c = 0; if ('0' <= S[i] and S[i] <= '9') { c = S[i] - '0'; } else if ('A' <= S[i] and S[i] <= 'F') { c = S[i] - 'A' + 10; } else { c = S[i] - 'a' + 10; } x = c + (x << 4); } dat.push_back(x); } _shrink(); } friend M operator+(const M& lhs, const M& rhs) { if (lhs.neg == rhs.neg) return {lhs.neg, _add(lhs.dat, rhs.dat)}; if (_leq(lhs.dat, rhs.dat)) { // |l| <= |r| auto c = _sub(rhs.dat, lhs.dat); bool n = _is_zero(c) ? false : rhs.neg; return {n, c}; } auto c = _sub(lhs.dat, rhs.dat); bool n = _is_zero(c) ? false : lhs.neg; return {n, c}; } friend M operator-(const M& lhs, const M& rhs) { return lhs + (-rhs); } friend M operator*(const M& lhs, const M& rhs) { auto c = _mul(lhs.dat, rhs.dat); bool n = _is_zero(c) ? false : (lhs.neg ^ rhs.neg); return {n, c}; } M& operator+=(const M& rhs) { return (*this) = (*this) + rhs; } M& operator-=(const M& rhs) { return (*this) = (*this) - rhs; } M& operator*=(const M& rhs) { return (*this) = (*this) * rhs; } M operator-() const { if (is_zero()) return *this; return {!neg, dat}; } M operator+() const { return *this; } friend M abs(const M& m) { return {false, m.dat}; } bool is_zero() const { return _is_zero(dat); } friend bool operator==(const M& lhs, const M& rhs) { return lhs.neg == rhs.neg && lhs.dat == rhs.dat; } friend bool operator!=(const M& lhs, const M& rhs) { return lhs.neg != rhs.neg || lhs.dat != rhs.dat; } friend bool operator<(const M& lhs, const M& rhs) { return lhs == rhs ? false : _neq_lt(lhs, rhs); } friend bool operator<=(const M& lhs, const M& rhs) { return lhs == rhs ? true : _neq_lt(lhs, rhs); } friend bool operator>(const M& lhs, const M& rhs) { return lhs == rhs ? false : _neq_lt(rhs, lhs); } friend bool operator>=(const M& lhs, const M& rhs) { return lhs == rhs ? true : _neq_lt(rhs, lhs); } // 0 の時 0 を返す int ctz() const { if (dat.empty()) return 0; int i = 0; while (dat[i] == 0) i++; return 32 * i + __builtin_ctzll(dat[i]); } M& operator<<=(int s) { assert(s >= 0); if (dat.empty()) return *this; int q = s / 32, r = s % 32; dat.push_back(0); if (r) { for (int i = (int)dat.size() - 1; i >= 1; i--) { dat[i] = (dat[i] << r) | (dat[i - 1] >> (32 - r)); } dat[0] <<= r; } dat.insert(begin(dat), q, 0); return *this; } M& operator>>=(int s) { assert(s >= 0); int q = s / 32, r = s % 32; if ((int)dat.size() <= q) { dat.clear(); return *this; } dat.erase(begin(dat), begin(dat) + q); if (r) { for (int i = 0; i + 1 < (int)dat.size(); i++) { dat[i] = (dat[i] >> r) | (dat[i + 1] << (32 - r)); } dat.back() >>= r; } _shrink(); return *this; } friend M gcd(M a, M b) { a.neg = b.neg = false; if(a.dat.empty()) return b; if(b.dat.empty()) return a; int at = a.ctz(), bt = b.ctz(); a >>= at, b >>= bt; if (a < b) swap(a, b); while (!b.dat.empty()) { a -= b; a >>= a.ctz(); if (a < b) swap(a, b); } return a <<= min(at, bt); } string to_hex() const { if (dat.empty()) return "0"; string res; for (int i = 0; i < (int)dat.size(); i++) { u32 x = dat[i]; for (int j = 0; j < 8; j++) { res.push_back("0123456789ABCDEF"[x & 15]); x >>= 4; } } while (res.back() == '0') res.pop_back(); reverse(begin(res), end(res)); if (neg) res.insert(begin(res), '-'); return res; } private: // size int _size() const { return dat.size(); } // a == b static bool _eq(const vector<u32>& a, const vector<u32>& b) { return a == b; } // a < b static bool _lt(const vector<u32>& a, const vector<u32>& b) { if (a.size() != b.size()) return a.size() < b.size(); for (int i = a.size() - 1; i >= 0; i--) { if (a[i] != b[i]) return a[i] < b[i]; } return false; } // a <= b static bool _leq(const vector<u32>& a, const vector<u32>& b) { return _eq(a, b) || _lt(a, b); } // a < b (s.t. a != b) static bool _neq_lt(const M& lhs, const M& rhs) { assert(lhs != rhs); if (lhs.neg != rhs.neg) return lhs.neg; bool f = _lt(lhs.dat, rhs.dat); if (f) return !lhs.neg; return lhs.neg; } // a == 0 static bool _is_zero(const vector<u32>& a) { return a.empty(); } // 末尾 0 を削除 static void _shrink(vector<u32>& a) { while (a.size() && a.back() == 0) a.pop_back(); } // 末尾 0 を削除 void _shrink() { while (_size() && dat.back() == 0) dat.pop_back(); } // a + b static vector<u32> _add(const vector<u32>& a, const vector<u32>& b) { vector<u32> c(max(a.size(), b.size()) + 1); int carry = 0; for (int i = 0; i < (int)c.size(); i++) { u64 s = carry; carry = 0; if (i < (int)a.size()) s += a[i]; if (i < (int)b.size()) s += b[i]; if (s >= (1uLL << 32)) s -= 1uLL << 32, carry = 1; c[i] = s; } _shrink(c); return c; } // a - b static vector<u32> _sub(const vector<u32>& a, const vector<u32>& b) { assert(_leq(b, a)); vector<u32> c{a}; i64 borrow = 0; for (int i = 0; i < (int)a.size(); i++) { if (i < (int)b.size()) borrow += b[i]; i64 x = c[i] - borrow; borrow = 0; if (x < 0) x += 1uLL << 32, borrow = 1; c[i] = x; } assert(borrow == 0); _shrink(c); return c; } // a * b (fft) static vector<u32> _mul(const vector<u32>& a, const vector<u32>& b) { if (a.empty() || b.empty()) return {}; vector<int> a2(a.size() * 2), b2(b.size() * 2); for (int i = 0; i < (int)a.size(); i++) { a2[i * 2 + 0] = a[i] & 65535; a2[i * 2 + 1] = a[i] >> 16; } for (int i = 0; i < (int)b.size(); i++) { b2[i * 2 + 0] = b[i] & 65535; b2[i * 2 + 1] = b[i] >> 16; } auto m = ArbitraryNTT::multiply_u128(a2, b2); vector<u32> c; c.reserve(a.size() + b.size() + 3); __uint128_t x = 0; for (int i = 0;; i += 2) { if (i >= (int)m.size() && x == 0) break; if (i + 0 < (int)m.size()) x += m[i + 0]; if (i + 1 < (int)m.size()) x += m[i + 1] << 16; c.push_back(x & ((1uLL << 32) - 1)); x >>= 32; } _shrink(c); return c; } }; } // namespace BinaryBigIntImpl using BinaryBigIntImpl::BinaryBigInt;
#line 1 "math/bigint-binary.hpp" #include <algorithm> #include <cassert> #include <cmath> #include <iostream> #include <tuple> #include <utility> #include <vector> using namespace std; #line 2 "ntt/arbitrary-ntt.hpp" #line 2 "modint/montgomery-modint.hpp" template <uint32_t mod> struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); static_assert(r * mod == 1, "this code has bugs."); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint operator+() const { return mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, u -= t * v; tmp = x, x = y, y = tmp; tmp = u, u = v, v = tmp; } return mint{u}; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt<mod>(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; #line 2 "ntt/ntt.hpp" template <typename mint> struct NTT { static constexpr uint32_t get_pr() { uint32_t _mod = mint::get_mod(); using u64 = uint64_t; u64 ds[32] = {}; int idx = 0; u64 m = _mod - 1; for (u64 i = 2; i * i <= m; ++i) { if (m % i == 0) { ds[idx++] = i; while (m % i == 0) m /= i; } } if (m != 1) ds[idx++] = m; uint32_t _pr = 2; while (1) { int flg = 1; for (int i = 0; i < idx; ++i) { u64 a = _pr, b = (_mod - 1) / ds[i], r = 1; while (b) { if (b & 1) r = r * a % _mod; a = a * a % _mod; b >>= 1; } if (r == 1) { flg = 0; break; } } if (flg == 1) break; ++_pr; } return _pr; }; static constexpr uint32_t mod = mint::get_mod(); static constexpr uint32_t pr = get_pr(); static constexpr int level = __builtin_ctzll(mod - 1); mint dw[level], dy[level]; void setwy(int k) { mint w[level], y[level]; w[k - 1] = mint(pr).pow((mod - 1) / (1 << k)); y[k - 1] = w[k - 1].inverse(); for (int i = k - 2; i > 0; --i) w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1]; dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2]; for (int i = 3; i < k; ++i) { dw[i] = dw[i - 1] * y[i - 2] * w[i]; dy[i] = dy[i - 1] * w[i - 2] * y[i]; } } NTT() { setwy(level); } void fft4(vector<mint> &a, int k) { if ((int)a.size() <= 1) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } if (k & 1) { int v = 1 << (k - 1); for (int j = 0; j < v; ++j) { mint ajv = a[j + v]; a[j + v] = a[j] - ajv; a[j] += ajv; } } int u = 1 << (2 + (k & 1)); int v = 1 << (k - 2 - (k & 1)); mint one = mint(1); mint imag = dw[1]; while (v) { // jh = 0 { int j0 = 0; int j1 = v; int j2 = j1 + v; int j3 = j2 + v; for (; j0 < v; ++j0, ++j1, ++j2, ++j3) { mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3]; mint t0p2 = t0 + t2, t1p3 = t1 + t3; mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3; } } // jh >= 1 mint ww = one, xx = one * dw[2], wx = one; for (int jh = 4; jh < u;) { ww = xx * xx, wx = ww * xx; int j0 = jh * v; int je = j0 + v; int j2 = je + v; for (; j0 < je; ++j0, ++j2) { mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww, t3 = a[j2 + v] * wx; mint t0p2 = t0 + t2, t1p3 = t1 + t3; mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3; } xx *= dw[__builtin_ctzll((jh += 4))]; } u <<= 2; v >>= 2; } } void ifft4(vector<mint> &a, int k) { if ((int)a.size() <= 1) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } int u = 1 << (k - 2); int v = 1; mint one = mint(1); mint imag = dy[1]; while (u) { // jh = 0 { int j0 = 0; int j1 = v; int j2 = v + v; int j3 = j2 + v; for (; j0 < v; ++j0, ++j1, ++j2, ++j3) { mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag; a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3; a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3; } } // jh >= 1 mint ww = one, xx = one * dy[2], yy = one; u <<= 2; for (int jh = 4; jh < u;) { ww = xx * xx, yy = xx * imag; int j0 = jh * v; int je = j0 + v; int j2 = je + v; for (; j0 < je; ++j0, ++j2) { mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v]; mint t0p1 = t0 + t1, t2p3 = t2 + t3; mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy; a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww; a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww; } xx *= dy[__builtin_ctzll(jh += 4)]; } u >>= 4; v <<= 2; } if (k & 1) { u = 1 << (k - 1); for (int j = 0; j < u; ++j) { mint ajv = a[j] - a[j + u]; a[j] += a[j + u]; a[j + u] = ajv; } } } void ntt(vector<mint> &a) { if ((int)a.size() <= 1) return; fft4(a, __builtin_ctz(a.size())); } void intt(vector<mint> &a) { if ((int)a.size() <= 1) return; ifft4(a, __builtin_ctz(a.size())); mint iv = mint(a.size()).inverse(); for (auto &x : a) x *= iv; } vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) { int l = a.size() + b.size() - 1; if (min<int>(a.size(), b.size()) <= 40) { vector<mint> s(l); for (int i = 0; i < (int)a.size(); ++i) for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j]; return s; } int k = 2, M = 4; while (M < l) M <<= 1, ++k; setwy(k); vector<mint> s(M); for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i]; fft4(s, k); if (a.size() == b.size() && a == b) { for (int i = 0; i < M; ++i) s[i] *= s[i]; } else { vector<mint> t(M); for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i]; fft4(t, k); for (int i = 0; i < M; ++i) s[i] *= t[i]; } ifft4(s, k); s.resize(l); mint invm = mint(M).inverse(); for (int i = 0; i < l; ++i) s[i] *= invm; return s; } void ntt_doubling(vector<mint> &a) { int M = (int)a.size(); auto b = a; intt(b); mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1)); for (int i = 0; i < M; i++) b[i] *= r, r *= zeta; ntt(b); copy(begin(b), end(b), back_inserter(a)); } }; #line 5 "ntt/arbitrary-ntt.hpp" namespace ArbitraryNTT { using i64 = int64_t; using u128 = __uint128_t; constexpr int32_t m0 = 167772161; constexpr int32_t m1 = 469762049; constexpr int32_t m2 = 754974721; using mint0 = LazyMontgomeryModInt<m0>; using mint1 = LazyMontgomeryModInt<m1>; using mint2 = LazyMontgomeryModInt<m2>; constexpr int r01 = mint1(m0).inverse().get(); constexpr int r02 = mint2(m0).inverse().get(); constexpr int r12 = mint2(m1).inverse().get(); constexpr int r02r12 = i64(r02) * r12 % m2; constexpr i64 w1 = m0; constexpr i64 w2 = i64(m0) * m1; template <typename T, typename submint> vector<submint> mul(const vector<T> &a, const vector<T> &b) { static NTT<submint> ntt; vector<submint> s(a.size()), t(b.size()); for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod()); for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod()); return ntt.multiply(s, t); } template <typename T> vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) { auto d0 = mul<T, mint0>(s, t); auto d1 = mul<T, mint1>(s, t); auto d2 = mul<T, mint2>(s, t); int n = d0.size(); vector<int> ret(n); const int W1 = w1 % mod; const int W2 = w2 % mod; for (int i = 0; i < n; i++) { int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get(); int b = i64(n1 + m1 - a) * r01 % m1; int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2; ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod; } return ret; } template <typename mint> vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) { if (a.size() == 0 && b.size() == 0) return {}; if (min<int>(a.size(), b.size()) < 128) { vector<mint> ret(a.size() + b.size() - 1); for (int i = 0; i < (int)a.size(); ++i) for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j]; return ret; } vector<int> s(a.size()), t(b.size()); for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get(); for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get(); vector<int> u = multiply<int>(s, t, mint::get_mod()); vector<mint> ret(u.size()); for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]); return ret; } template <typename T> vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) { if (s.size() == 0 && t.size() == 0) return {}; if (min<int>(s.size(), t.size()) < 128) { vector<u128> ret(s.size() + t.size() - 1); for (int i = 0; i < (int)s.size(); ++i) for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j]; return ret; } auto d0 = mul<T, mint0>(s, t); auto d1 = mul<T, mint1>(s, t); auto d2 = mul<T, mint2>(s, t); int n = d0.size(); vector<u128> ret(n); for (int i = 0; i < n; i++) { i64 n1 = d1[i].get(), n2 = d2[i].get(); i64 a = d0[i].get(); i64 b = (n1 + m1 - a) * r01 % m1; i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2; ret[i] = a + b * w1 + u128(c) * w2; } return ret; } } // namespace ArbitraryNTT #line 12 "math/bigint-binary.hpp" namespace BinaryBigIntImpl { using u32 = unsigned int; using u64 = unsigned long long; using i64 = long long; // 0 は neg=false, dat={} として扱う struct BinaryBigInt { using M = BinaryBigInt; bool neg; vector<u32> dat; BinaryBigInt() : neg(false), dat() {} BinaryBigInt(bool _neg, const vector<u32>& _dat) : neg(_neg), dat(_dat) {} BinaryBigInt(const string& S, int base) : neg(false) { assert(base == 16); int ie = -1; if (S[0] == '-') neg = true, ie++; for (int r = S.size() - 1; r > ie; r -= 8) { int l = max(r - 8, ie); u32 x = 0; for (int i = l + 1; i <= r; i++) { int c = 0; if ('0' <= S[i] and S[i] <= '9') { c = S[i] - '0'; } else if ('A' <= S[i] and S[i] <= 'F') { c = S[i] - 'A' + 10; } else { c = S[i] - 'a' + 10; } x = c + (x << 4); } dat.push_back(x); } _shrink(); } friend M operator+(const M& lhs, const M& rhs) { if (lhs.neg == rhs.neg) return {lhs.neg, _add(lhs.dat, rhs.dat)}; if (_leq(lhs.dat, rhs.dat)) { // |l| <= |r| auto c = _sub(rhs.dat, lhs.dat); bool n = _is_zero(c) ? false : rhs.neg; return {n, c}; } auto c = _sub(lhs.dat, rhs.dat); bool n = _is_zero(c) ? false : lhs.neg; return {n, c}; } friend M operator-(const M& lhs, const M& rhs) { return lhs + (-rhs); } friend M operator*(const M& lhs, const M& rhs) { auto c = _mul(lhs.dat, rhs.dat); bool n = _is_zero(c) ? false : (lhs.neg ^ rhs.neg); return {n, c}; } M& operator+=(const M& rhs) { return (*this) = (*this) + rhs; } M& operator-=(const M& rhs) { return (*this) = (*this) - rhs; } M& operator*=(const M& rhs) { return (*this) = (*this) * rhs; } M operator-() const { if (is_zero()) return *this; return {!neg, dat}; } M operator+() const { return *this; } friend M abs(const M& m) { return {false, m.dat}; } bool is_zero() const { return _is_zero(dat); } friend bool operator==(const M& lhs, const M& rhs) { return lhs.neg == rhs.neg && lhs.dat == rhs.dat; } friend bool operator!=(const M& lhs, const M& rhs) { return lhs.neg != rhs.neg || lhs.dat != rhs.dat; } friend bool operator<(const M& lhs, const M& rhs) { return lhs == rhs ? false : _neq_lt(lhs, rhs); } friend bool operator<=(const M& lhs, const M& rhs) { return lhs == rhs ? true : _neq_lt(lhs, rhs); } friend bool operator>(const M& lhs, const M& rhs) { return lhs == rhs ? false : _neq_lt(rhs, lhs); } friend bool operator>=(const M& lhs, const M& rhs) { return lhs == rhs ? true : _neq_lt(rhs, lhs); } // 0 の時 0 を返す int ctz() const { if (dat.empty()) return 0; int i = 0; while (dat[i] == 0) i++; return 32 * i + __builtin_ctzll(dat[i]); } M& operator<<=(int s) { assert(s >= 0); if (dat.empty()) return *this; int q = s / 32, r = s % 32; dat.push_back(0); if (r) { for (int i = (int)dat.size() - 1; i >= 1; i--) { dat[i] = (dat[i] << r) | (dat[i - 1] >> (32 - r)); } dat[0] <<= r; } dat.insert(begin(dat), q, 0); return *this; } M& operator>>=(int s) { assert(s >= 0); int q = s / 32, r = s % 32; if ((int)dat.size() <= q) { dat.clear(); return *this; } dat.erase(begin(dat), begin(dat) + q); if (r) { for (int i = 0; i + 1 < (int)dat.size(); i++) { dat[i] = (dat[i] >> r) | (dat[i + 1] << (32 - r)); } dat.back() >>= r; } _shrink(); return *this; } friend M gcd(M a, M b) { a.neg = b.neg = false; if(a.dat.empty()) return b; if(b.dat.empty()) return a; int at = a.ctz(), bt = b.ctz(); a >>= at, b >>= bt; if (a < b) swap(a, b); while (!b.dat.empty()) { a -= b; a >>= a.ctz(); if (a < b) swap(a, b); } return a <<= min(at, bt); } string to_hex() const { if (dat.empty()) return "0"; string res; for (int i = 0; i < (int)dat.size(); i++) { u32 x = dat[i]; for (int j = 0; j < 8; j++) { res.push_back("0123456789ABCDEF"[x & 15]); x >>= 4; } } while (res.back() == '0') res.pop_back(); reverse(begin(res), end(res)); if (neg) res.insert(begin(res), '-'); return res; } private: // size int _size() const { return dat.size(); } // a == b static bool _eq(const vector<u32>& a, const vector<u32>& b) { return a == b; } // a < b static bool _lt(const vector<u32>& a, const vector<u32>& b) { if (a.size() != b.size()) return a.size() < b.size(); for (int i = a.size() - 1; i >= 0; i--) { if (a[i] != b[i]) return a[i] < b[i]; } return false; } // a <= b static bool _leq(const vector<u32>& a, const vector<u32>& b) { return _eq(a, b) || _lt(a, b); } // a < b (s.t. a != b) static bool _neq_lt(const M& lhs, const M& rhs) { assert(lhs != rhs); if (lhs.neg != rhs.neg) return lhs.neg; bool f = _lt(lhs.dat, rhs.dat); if (f) return !lhs.neg; return lhs.neg; } // a == 0 static bool _is_zero(const vector<u32>& a) { return a.empty(); } // 末尾 0 を削除 static void _shrink(vector<u32>& a) { while (a.size() && a.back() == 0) a.pop_back(); } // 末尾 0 を削除 void _shrink() { while (_size() && dat.back() == 0) dat.pop_back(); } // a + b static vector<u32> _add(const vector<u32>& a, const vector<u32>& b) { vector<u32> c(max(a.size(), b.size()) + 1); int carry = 0; for (int i = 0; i < (int)c.size(); i++) { u64 s = carry; carry = 0; if (i < (int)a.size()) s += a[i]; if (i < (int)b.size()) s += b[i]; if (s >= (1uLL << 32)) s -= 1uLL << 32, carry = 1; c[i] = s; } _shrink(c); return c; } // a - b static vector<u32> _sub(const vector<u32>& a, const vector<u32>& b) { assert(_leq(b, a)); vector<u32> c{a}; i64 borrow = 0; for (int i = 0; i < (int)a.size(); i++) { if (i < (int)b.size()) borrow += b[i]; i64 x = c[i] - borrow; borrow = 0; if (x < 0) x += 1uLL << 32, borrow = 1; c[i] = x; } assert(borrow == 0); _shrink(c); return c; } // a * b (fft) static vector<u32> _mul(const vector<u32>& a, const vector<u32>& b) { if (a.empty() || b.empty()) return {}; vector<int> a2(a.size() * 2), b2(b.size() * 2); for (int i = 0; i < (int)a.size(); i++) { a2[i * 2 + 0] = a[i] & 65535; a2[i * 2 + 1] = a[i] >> 16; } for (int i = 0; i < (int)b.size(); i++) { b2[i * 2 + 0] = b[i] & 65535; b2[i * 2 + 1] = b[i] >> 16; } auto m = ArbitraryNTT::multiply_u128(a2, b2); vector<u32> c; c.reserve(a.size() + b.size() + 3); __uint128_t x = 0; for (int i = 0;; i += 2) { if (i >= (int)m.size() && x == 0) break; if (i + 0 < (int)m.size()) x += m[i + 0]; if (i + 1 < (int)m.size()) x += m[i + 1] << 16; c.push_back(x & ((1uLL << 32) - 1)); x >>= 32; } _shrink(c); return c; } }; } // namespace BinaryBigIntImpl using BinaryBigIntImpl::BinaryBigInt;