algo/math/modint.h

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• Last update: 2026-07-26 15:26:45-04:00

Depends on

• algo/common.h
• algo/math/common.h

Required by

• main.cpp

Verified with

• verify/ds/lazy_segtree.test.cpp
• verify/math/combo.test.cpp

Code

#pragma once
#include "algo/common.h"
#include "algo/math/common.h"

namespace algo::math {

// A modulus fixed at compile time: no state, and the division folds into a
// multiply-shift.
template <int Mod>
struct static_mod {
    static constexpr int mod() {
        return Mod;
    }
    static int reduce(uint64_t x) {
        return (int)(x % (uint64_t)Mod);
    }
};

// A modulus known only at run time, held for the extent of with_mod. Nesting is
// rejected: values built under the outer modulus would survive into the inner
// one. Use a second id to hold two moduli at once.
template <int id>
struct dynamic_mod {
    static int mod() {
        assert(armed);
        return bt.mod();
    }
    static int reduce(uint64_t x) {
        return (int)bt.reduce(x);
    }
    static auto with_mod(int m, auto callback) {
        assert(1 <= m && !armed);
        struct scoped {
            ~scoped() {
                armed = false;
            }
        } _;
        bt = barrett(m), armed = true;
        return callback();
    }

private:
    static inline barrett bt{1};
    static inline bool armed = false;
};

// P supplies mod() and reduce(). Inheriting it makes both reachable through the
// modint (as is with_mod), and an empty policy costs no space.
template <typename P>
struct modint : P {
    modint() : v(0) {
    }
    modint(int64_t _v) {
        v = (-P::mod() < _v && _v < P::mod()) ? _v : _v % P::mod();
        if (v < 0) v += P::mod();
    }
    modint &operator+=(const modint &other) {
        v += other.v;
        if (v >= P::mod()) v -= P::mod();
        return *this;
    }
    modint &operator-=(const modint &other) {
        v -= other.v;
        if (v < 0) v += P::mod();
        return *this;
    }
    modint &operator*=(const modint &other) {
        v = P::reduce((uint64_t)v * other.v);
        return *this;
    }
    modint &operator/=(const modint &other) {
        return *this = *this * other.inv();
    }
    modint &operator++() {
        v++;
        if (v == P::mod()) v = 0;
        return *this;
    }
    modint &operator--() {
        if (v == 0) v = P::mod();
        v--;
        return *this;
    }
    modint operator++(int) {
        modint result = *this;
        ++*this;
        return result;
    }
    modint operator--(int) {
        modint result = *this;
        --*this;
        return result;
    }
    friend modint operator+(modint a, const modint &b) {
        return a += b;
    }
    friend modint operator-(modint a, const modint &b) {
        return a -= b;
    }
    friend modint operator*(modint a, const modint &b) {
        return a *= b;
    }
    friend modint operator/(modint a, const modint &b) {
        return a /= b;
    }
    friend modint operator-(modint a) {
        return 0 - a;
    }
    modint inv() const {
        auto eg = inv_gcd(v, P::mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend bool operator==(const modint &a, const modint &b) {
        return a.v == b.v;
    }
    friend bool operator!=(const modint &a, const modint &b) {
        return !(a == b);
    }
    explicit operator int() const {
        return v;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &a) {
        return os << a.v;
    }
    friend std::istream &operator>>(std::istream &is, modint &a) {
        is >> a.v;
        a.v = (-P::mod() < a.v && a.v < P::mod()) ? a.v : a.v % P::mod();
        if (a.v < 0) a.v += P::mod();
        return is;
    }

private:
    int v;
};

template <int Mod>
using static_modint = modint<static_mod<Mod>>;
template <int id = 0>
using dynamic_modint = modint<dynamic_mod<id>>;

} // namespace algo::math

#line 2 "algo/common.h"
#ifndef PREPROCESS
#include <bits/stdc++.h>
#include <cassert>
#endif

namespace algo {

// Indices and sizes into library containers. Signed, so the usual "walk down to
// -1" loops still terminate; widening the whole library is a change here alone.
using index_t = int;

} // namespace algo
#line 3 "algo/math/common.h"

namespace algo::math {

constexpr int64_t safe_mod(int64_t x, int64_t m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Returns (x ** n) % m
constexpr int64_t pow_mod_constexpr(int64_t x, int64_t n, int m) {
    assert(0 <= n);
    assert(1 <= m);
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    uint64_t r = 1;
    uint64_t y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

struct barrett {
    constexpr explicit barrett(uint64_t _m) : m(_m), im(-1ULL / _m) {
        assert(1 <= _m);
    }
    uint64_t mod() const {
        return m;
    };
    uint64_t reduce(uint64_t a) const {
        uint64_t q = (uint64_t)((__uint128_t(im) * a) >> 64);
        uint64_t r = a - q * m;
        return r - (r >= m) * m;
    }

private:
    uint64_t m, im;
};

constexpr int64_t c_div(int64_t a, int64_t b) {
    return a / b + ((a ^ b) > 0 && a % b);
}
constexpr int64_t f_div(int64_t a, int64_t b) {
    return a / b - ((a ^ b) < 0 && a % b);
}

auto bpow(auto const &x, auto n, auto const &one, auto op) {
    if (n == 0) {
        return one;
    } else {
        auto t = bpow(x, n / 2, one, op);
        t = op(t, t);
        if (n % 2) {
            t = op(t, x);
        }
        return t;
    }
}
auto bpow(auto x, auto n, auto ans) {
    return bpow(x, n, ans, std::multiplies{});
}
template <typename T>
T bpow(T const &x, auto n) {
    return bpow(x, n, T(1));
}

// Returns a pair(g, x) s.t. g = gcd(a, n), xa = g (mod n), 0 <= x < n/g
// If r > 1 then a is not invertible mod n
constexpr std::pair<int64_t, int64_t> inv_gcd(int64_t a, int64_t n) {
    a = safe_mod(a, n);
    if (a == 0) return {n, 0};

    int64_t t = 0, newt = 1;
    int64_t r = n, newr = a;

    while (newr) {
        int64_t quotient = r / newr;
        r -= newr * quotient;
        t -= newt * quotient;

        std::swap(r, newr);
        std::swap(t, newt);
    }
    if (t < 0) t += n / r;
    return {r, t};
}

} // namespace algo::math
#line 4 "algo/math/modint.h"

namespace algo::math {

// A modulus fixed at compile time: no state, and the division folds into a
// multiply-shift.
template <int Mod>
struct static_mod {
    static constexpr int mod() {
        return Mod;
    }
    static int reduce(uint64_t x) {
        return (int)(x % (uint64_t)Mod);
    }
};

// A modulus known only at run time, held for the extent of with_mod. Nesting is
// rejected: values built under the outer modulus would survive into the inner
// one. Use a second id to hold two moduli at once.
template <int id>
struct dynamic_mod {
    static int mod() {
        assert(armed);
        return bt.mod();
    }
    static int reduce(uint64_t x) {
        return (int)bt.reduce(x);
    }
    static auto with_mod(int m, auto callback) {
        assert(1 <= m && !armed);
        struct scoped {
            ~scoped() {
                armed = false;
            }
        } _;
        bt = barrett(m), armed = true;
        return callback();
    }

private:
    static inline barrett bt{1};
    static inline bool armed = false;
};

// P supplies mod() and reduce(). Inheriting it makes both reachable through the
// modint (as is with_mod), and an empty policy costs no space.
template <typename P>
struct modint : P {
    modint() : v(0) {
    }
    modint(int64_t _v) {
        v = (-P::mod() < _v && _v < P::mod()) ? _v : _v % P::mod();
        if (v < 0) v += P::mod();
    }
    modint &operator+=(const modint &other) {
        v += other.v;
        if (v >= P::mod()) v -= P::mod();
        return *this;
    }
    modint &operator-=(const modint &other) {
        v -= other.v;
        if (v < 0) v += P::mod();
        return *this;
    }
    modint &operator*=(const modint &other) {
        v = P::reduce((uint64_t)v * other.v);
        return *this;
    }
    modint &operator/=(const modint &other) {
        return *this = *this * other.inv();
    }
    modint &operator++() {
        v++;
        if (v == P::mod()) v = 0;
        return *this;
    }
    modint &operator--() {
        if (v == 0) v = P::mod();
        v--;
        return *this;
    }
    modint operator++(int) {
        modint result = *this;
        ++*this;
        return result;
    }
    modint operator--(int) {
        modint result = *this;
        --*this;
        return result;
    }
    friend modint operator+(modint a, const modint &b) {
        return a += b;
    }
    friend modint operator-(modint a, const modint &b) {
        return a -= b;
    }
    friend modint operator*(modint a, const modint &b) {
        return a *= b;
    }
    friend modint operator/(modint a, const modint &b) {
        return a /= b;
    }
    friend modint operator-(modint a) {
        return 0 - a;
    }
    modint inv() const {
        auto eg = inv_gcd(v, P::mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend bool operator==(const modint &a, const modint &b) {
        return a.v == b.v;
    }
    friend bool operator!=(const modint &a, const modint &b) {
        return !(a == b);
    }
    explicit operator int() const {
        return v;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &a) {
        return os << a.v;
    }
    friend std::istream &operator>>(std::istream &is, modint &a) {
        is >> a.v;
        a.v = (-P::mod() < a.v && a.v < P::mod()) ? a.v : a.v % P::mod();
        if (a.v < 0) a.v += P::mod();
        return is;
    }

private:
    int v;
};

template <int Mod>
using static_modint = modint<static_mod<Mod>>;
template <int id = 0>
using dynamic_modint = modint<dynamic_mod<id>>;

} // namespace algo::math

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