other/mint.hpp

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• Last update: 2022-11-02 07:08:37+09:00
• Include: #include "other/mint.hpp"

Required by

• test/atcoder/ABC129_E.cpp
• test/atcoder/ABC129_E_2.cpp
• test/atcoder/ABC138_F.cpp
• test/atcoder/ABC154_E.cpp
• test/atcoder/ABC235_F.cpp
• test/atcoder/EDPC_S.cpp

Verified with

• test/aoj/0570.test.cpp
• test/yukicoder/0315.test.cpp
• test/yukicoder/0685.test.cpp
• test/yukicoder/1417.test.cpp
• test/yukicoder/1740.test.cpp

Code

#pragma once

template< int MOD >
struct mint {
public:
    unsigned int x;
    mint() : x(0) {}
    mint(long long v) {
        long long w = (long long)(v % (long long)(MOD));
        if (w < 0) w += MOD;
        x = (unsigned int)(w);
    }
    mint(std::string &s) {
        unsigned int z = 0;
        for (int i = 0; i < s.size(); i++) {
            z *= 10;
            z += s[i] - '0';
            z %= MOD;
        }
        x = z;
    }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint& operator+=(const mint &a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator-=(const mint &a) {
        if ((x -= a.x) >= MOD) x += MOD;
        return *this;
    }
    mint& operator*=(const mint &a) {
        unsigned long long z = x;
        z *= a.x;
        x = (unsigned int)(z % MOD);
        return *this;
    }
    mint& operator/=(const mint &a) {return *this = *this * a.inv(); }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs.x != rhs.x;
    }
    friend std::ostream& operator<<(std::ostream &os, const mint &n) {
        return os << n.x;
    }
    friend std::istream &operator>>(std::istream &is, mint &n) {
        unsigned int x;
        is >> x;
        n = mint(x);
        return is;
    }
    mint inv() const {
        assert(x);
        return pow(MOD-2);
    }
    mint pow(long long n) const {        
        assert(0 <= n);
        mint p = *this, r = 1;
        while (n) {
            if (n & 1) r *= p;
            p *= p;
            n >>= 1;
        }
        return r;
    }
    
    // 存在しない場合0を返す(二乗して確認).
    // O(log^2MOD)
    mint sqrt() const {
        if (this->x < 2) return *this;
        if (this->pow((MOD-1)>>1).x != 1) return mint(0);
        mint b = 1, one = 1;
        while (b.pow((MOD-1) >> 1) == 1) b += one;
        long long m = MOD-1, e = 0;
        while (m % 2 == 0) m >>= 1, e += 1;
        mint x = this->pow((m - 1) >> 1);
        mint y = (*this) * x * x;
        x *= (*this);
        mint z = b.pow(m);
        while (y.x != 1) {
            int j = 0;
            mint t = y;
            while (t != one) j += 1, t *= t;
            z = z.pow(1LL << (e-j-1));
            x *= z; z *= z; y *= z; e = j;
        }
        return x;
    }
};

#line 2 "other/mint.hpp"

template< int MOD >
struct mint {
public:
    unsigned int x;
    mint() : x(0) {}
    mint(long long v) {
        long long w = (long long)(v % (long long)(MOD));
        if (w < 0) w += MOD;
        x = (unsigned int)(w);
    }
    mint(std::string &s) {
        unsigned int z = 0;
        for (int i = 0; i < s.size(); i++) {
            z *= 10;
            z += s[i] - '0';
            z %= MOD;
        }
        x = z;
    }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint& operator+=(const mint &a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator-=(const mint &a) {
        if ((x -= a.x) >= MOD) x += MOD;
        return *this;
    }
    mint& operator*=(const mint &a) {
        unsigned long long z = x;
        z *= a.x;
        x = (unsigned int)(z % MOD);
        return *this;
    }
    mint& operator/=(const mint &a) {return *this = *this * a.inv(); }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs.x != rhs.x;
    }
    friend std::ostream& operator<<(std::ostream &os, const mint &n) {
        return os << n.x;
    }
    friend std::istream &operator>>(std::istream &is, mint &n) {
        unsigned int x;
        is >> x;
        n = mint(x);
        return is;
    }
    mint inv() const {
        assert(x);
        return pow(MOD-2);
    }
    mint pow(long long n) const {        
        assert(0 <= n);
        mint p = *this, r = 1;
        while (n) {
            if (n & 1) r *= p;
            p *= p;
            n >>= 1;
        }
        return r;
    }
    
    // 存在しない場合0を返す(二乗して確認).
    // O(log^2MOD)
    mint sqrt() const {
        if (this->x < 2) return *this;
        if (this->pow((MOD-1)>>1).x != 1) return mint(0);
        mint b = 1, one = 1;
        while (b.pow((MOD-1) >> 1) == 1) b += one;
        long long m = MOD-1, e = 0;
        while (m % 2 == 0) m >>= 1, e += 1;
        mint x = this->pow((m - 1) >> 1);
        mint y = (*this) * x * x;
        x *= (*this);
        mint z = b.pow(m);
        while (y.x != 1) {
            int j = 0;
            mint t = y;
            while (t != one) j += 1, t *= t;
            z = z.pow(1LL << (e-j-1));
            x *= z; z *= z; y *= z; e = j;
        }
        return x;
    }
};

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