library/mod/Modint.hpp

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• Last update: 2025-11-24 18:49:07+09:00
• Include: #include "library/mod/Modint.hpp"

Depends on

• build/pch/stdc++.hpp
• library/math/ExtraGCD.hpp

Required by

• library/formalpowerseries/Sqrt.hpp
• library/math/ModularSqrt.hpp

Verified with

• test/AOJ/2971.test.cpp
• test/library-checker/Convolution/BitwiseAndConvolution.test.cpp
• test/library-checker/Convolution/BitwiseXorConvolution.test.cpp
• test/library-checker/Convolution/SubsetConvolution.test.cpp
• test/library-checker/DataStructure/PointSetRangeComposite.test.cpp
• test/library-checker/DataStructure/QueueOperateAllComposite.test.cpp
• test/library-checker/DataStructure/RangeAffineRangeSum.test.cpp
• test/library-checker/Matrix/Det.test.cpp
• test/library-checker/Matrix/Inverse.test.cpp
• test/library-checker/Matrix/Product.test.cpp
• test/library-checker/New/NumberOfSubsequence.test.cpp
• test/library-checker/Polynomial/Convolution.test.cpp
• test/library-checker/Tree/vertex_set_path_composite.test.cpp
• test/yukicoder/117.test.cpp
• test/yukicoder/1502.test.cpp
• test/yukicoder/650.test.cpp

Code

#pragma once
#include "library/math/ExtraGCD.hpp"
template <typename T, T MOD = 998244353> struct Mint {
    inline static constexpr T mod = MOD;
    T v;
    Mint() : v(0) {}
    Mint(signed v) : v(v) {}
    Mint(long long t) {
        v = t % MOD;
        if (v < 0)
            v += MOD;
    }

    static Mint raw(int v) {
        Mint x;
        x.v = v;
        return x;
    }

    Mint pow(long long k) const {
        Mint res(1), tmp(v);
        while (k) {
            if (k & 1)
                res *= tmp;
            tmp *= tmp;
            k >>= 1;
        }
        return res;
    }

    static Mint add_identity() { return Mint(0); }
    static Mint mul_identity() { return Mint(1); }

    // Mint inv()const{return pow(MOD-2);}
    Mint inv() const { return Mint(ext_gcd(v, mod).first); }

    Mint &operator+=(Mint a) {
        v += a.v;
        if (v >= MOD)
            v -= MOD;
        return *this;
    }
    Mint &operator-=(Mint a) {
        v += MOD - a.v;
        if (v >= MOD)
            v -= MOD;
        return *this;
    }
    Mint &operator*=(Mint a) {
        v = 1LL * v * a.v % MOD;
        return *this;
    }
    Mint &operator/=(Mint a) { return (*this) *= a.inv(); }

    Mint operator+(Mint a) const { return Mint(v) += a; }
    Mint operator-(Mint a) const { return Mint(v) -= a; }
    Mint operator*(Mint a) const { return Mint(v) *= a; }
    Mint operator/(Mint a) const { return Mint(v) /= a; }
#define FRIEND(op)                                                             \
    friend Mint operator op(int a, Mint b) { return Mint(a) op b; }
    FRIEND(+);
    FRIEND(-);
    FRIEND(*);
    FRIEND(/);
#undef FRIEND
    Mint operator+() const { return *this; }
    Mint operator-() const { return v ? Mint(MOD - v) : Mint(v); }

    bool operator==(const Mint a) const { return v == a.v; }
    bool operator!=(const Mint a) const { return v != a.v; }

    static Mint comb(long long n, int k) {
        Mint num(1), dom(1);
        for (int i = 0; i < k; i++) {
            num *= Mint(n - i);
            dom *= Mint(i + 1);
        }
        return num / dom;
    }

    friend std::ostream &operator<<(std::ostream &os, const Mint &m) {
        os << m.v;
        return os;
    }
    friend std::istream &operator>>(std::istream &is, Mint &m) {
        is >> m.v;
        m.v %= MOD;
        if (m.v < 0)
            m.v += MOD;
        return is;
    }
};

#line 2 "library/math/ExtraGCD.hpp"
using ll = long long;
std::pair<ll, ll> ext_gcd(ll a, ll b) {
    if (b == 0)
        return {1, 0};
    auto [X, Y] = ext_gcd(b, a % b);
    // bX + (a%b)Y = gcd(a,b)
    // a%b = a - b(a/b)
    // ∴ aY + b(X-(a/b)Y) = gcd(a,b)
    ll x = Y, y = X - (a / b) * Y;
    return {x, y};
}
#line 3 "library/mod/Modint.hpp"
template <typename T, T MOD = 998244353> struct Mint {
    inline static constexpr T mod = MOD;
    T v;
    Mint() : v(0) {}
    Mint(signed v) : v(v) {}
    Mint(long long t) {
        v = t % MOD;
        if (v < 0)
            v += MOD;
    }

    static Mint raw(int v) {
        Mint x;
        x.v = v;
        return x;
    }

    Mint pow(long long k) const {
        Mint res(1), tmp(v);
        while (k) {
            if (k & 1)
                res *= tmp;
            tmp *= tmp;
            k >>= 1;
        }
        return res;
    }

    static Mint add_identity() { return Mint(0); }
    static Mint mul_identity() { return Mint(1); }

    // Mint inv()const{return pow(MOD-2);}
    Mint inv() const { return Mint(ext_gcd(v, mod).first); }

    Mint &operator+=(Mint a) {
        v += a.v;
        if (v >= MOD)
            v -= MOD;
        return *this;
    }
    Mint &operator-=(Mint a) {
        v += MOD - a.v;
        if (v >= MOD)
            v -= MOD;
        return *this;
    }
    Mint &operator*=(Mint a) {
        v = 1LL * v * a.v % MOD;
        return *this;
    }
    Mint &operator/=(Mint a) { return (*this) *= a.inv(); }

    Mint operator+(Mint a) const { return Mint(v) += a; }
    Mint operator-(Mint a) const { return Mint(v) -= a; }
    Mint operator*(Mint a) const { return Mint(v) *= a; }
    Mint operator/(Mint a) const { return Mint(v) /= a; }
#define FRIEND(op)                                                             \
    friend Mint operator op(int a, Mint b) { return Mint(a) op b; }
    FRIEND(+);
    FRIEND(-);
    FRIEND(*);
    FRIEND(/);
#undef FRIEND
    Mint operator+() const { return *this; }
    Mint operator-() const { return v ? Mint(MOD - v) : Mint(v); }

    bool operator==(const Mint a) const { return v == a.v; }
    bool operator!=(const Mint a) const { return v != a.v; }

    static Mint comb(long long n, int k) {
        Mint num(1), dom(1);
        for (int i = 0; i < k; i++) {
            num *= Mint(n - i);
            dom *= Mint(i + 1);
        }
        return num / dom;
    }

    friend std::ostream &operator<<(std::ostream &os, const Mint &m) {
        os << m.v;
        return os;
    }
    friend std::istream &operator>>(std::istream &is, Mint &m) {
        is >> m.v;
        m.v %= MOD;
        if (m.v < 0)
            m.v += MOD;
        return is;
    }
};

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