utility/modint4724.hpp

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• Last update: 2024-07-06 19:03:02+09:00
• Include: #include "utility/modint4724.hpp"

Depends on

• math/prime.hpp
• utility/modint.hpp

Verified with

• test/tree/FrequencyTableofTreeDistance.test.cpp

Code

#pragma once

#include "modint.hpp"

namespace noya2 {

template<>
struct static_modint<-4724> {
    static constexpr unsigned long long mod(){
        return m;
    }
    static constexpr unsigned long long cal_mod(unsigned long long x){
        unsigned long long xu = x >> 47;
        unsigned long long xd = x & MASK47;
        unsigned long long res = (xu << 24) + xd - xu;
        if (res >= m) res -= m;
        return res;
    }
    constexpr static_modint() : _v(0) {}
    constexpr static_modint(long long x){
        if (x < 0){
            _v = cal_mod(-x);
            if (_v != 0){
                _v = m - _v;
            }
        }
        else {
            _v = cal_mod(x);
        }
    }
    constexpr static_modint(unsigned long long x){
        _v = cal_mod(x);
    }
    template<std::signed_integral T>
    constexpr static_modint(T x) : static_modint((long long)x) {}
    template<std::unsigned_integral T>
    constexpr static_modint(T x) : static_modint((unsigned long long)x) {}
    
    using modint4724 = static_modint;
    constexpr modint4724 &operator+=(const modint4724 &p){
        _v += p._v;
        if (_v >= m) _v -= m;
        return *this;
    }
    constexpr modint4724 &operator-=(const modint4724 &p){
        _v += m - p._v;
        if (_v >= m) _v -= m;
        return *this;
    }
    constexpr modint4724 &operator*=(const modint4724 &p){
        unsigned long long a = _v, b = p._v;
        unsigned long long au = a >> 24, ad = a & MASK24;
        unsigned long long bu = b >> 24, bd = b & MASK24;
        unsigned long long X = (au + ad) * (bu + bd);
        unsigned long long Y = ad * bd;
        unsigned long long Z = au * bu;
        unsigned long long A = X - Y + Z, B = Y + m4 - 2*Z;
        unsigned long long Au = A >> 23, Ad = A & MASK23;
        _v = cal_mod(((Au + Ad) << 24) + B + m - Au);
        return *this;
    }
    constexpr modint4724 &operator/=(const modint4724 &p){
        *this *= p.inv();
        return *this;
    }
    friend constexpr modint4724 operator+(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) += rhs;
    }
    friend constexpr modint4724 operator-(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) -= rhs;
    }
    friend constexpr modint4724 operator*(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) *= rhs;
    }
    friend constexpr modint4724 operator/(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) /= rhs;
    }
    constexpr modint4724 operator+() const {
        return *this;
    }
    constexpr modint4724 operator-() const {
        return modint4724() - *this;
    }
    constexpr modint4724 inv() const {
        long long a = _v, b = m, u = 1, v = 0;
        while (b > 0){
            long long t = a / b;
            std::swap(a -= t * b, b);
            std::swap(u -= t * v, v);
        }
        return modint4724(u);
    }
    constexpr modint4724 pow(long long n) const {
        modint4724 ret(1ULL), mul(_v);
        while (n != 0){
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend std::istream &operator>>(std::istream &is, modint4724 &p){
        unsigned long long x;
        is >> x;
        p = modint4724(x);
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint4724 &p){
        return os << p._v;
    }
    constexpr unsigned long long val() const {
        return _v;
    }
    constexpr auto operator<=>(const modint4724 &) const = default;

  private:
    unsigned long long _v;
    static constexpr unsigned long long m = (1ULL << 47) - (1ULL << 24) + 1;
    static constexpr unsigned long long m4 = m << 2;
    static constexpr unsigned long long MASK23 = (1ULL << 23) - 1;
    static constexpr unsigned long long MASK24 = (1ULL << 24) - 1;
    static constexpr unsigned long long MASK47 = (1ULL << 47) - 1;
};
using modint4724 = static_modint<-4724>;

} // namespace noya2

#line 2 "utility/modint4724.hpp"

#line 2 "utility/modint.hpp"

#include <iostream>

#line 2 "math/prime.hpp"

#include<utility>
namespace noya2 {

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

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; 
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);

} // namespace noya2
#line 6 "utility/modint.hpp"

namespace noya2{

struct barrett {
    unsigned int _m;
    unsigned long long im;
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    unsigned int umod() const { return _m; }
    unsigned int mul(unsigned int a, unsigned int b) const {
        unsigned long long z = a;
        z *= b;
        unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

template <int m>
struct static_modint {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    constexpr static_modint() : _v(0) {}
    template<std::signed_integral T>
    constexpr static_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    constexpr static_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    constexpr unsigned int val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    constexpr mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (uint)(z % umod());
        return *this;
    }
    constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = is_prime_flag<m>;
};


template <int id> struct dynamic_modint {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template<std::signed_integral T>
    dynamic_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    dynamic_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    uint val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = noya2::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    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._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

template<typename T>
concept Modint = requires (T &a){
    T::mod();
    a.inv();
    a.val();
    a.pow(declval<int>());
};

} // namespace noya2
#line 4 "utility/modint4724.hpp"

namespace noya2 {

template<>
struct static_modint<-4724> {
    static constexpr unsigned long long mod(){
        return m;
    }
    static constexpr unsigned long long cal_mod(unsigned long long x){
        unsigned long long xu = x >> 47;
        unsigned long long xd = x & MASK47;
        unsigned long long res = (xu << 24) + xd - xu;
        if (res >= m) res -= m;
        return res;
    }
    constexpr static_modint() : _v(0) {}
    constexpr static_modint(long long x){
        if (x < 0){
            _v = cal_mod(-x);
            if (_v != 0){
                _v = m - _v;
            }
        }
        else {
            _v = cal_mod(x);
        }
    }
    constexpr static_modint(unsigned long long x){
        _v = cal_mod(x);
    }
    template<std::signed_integral T>
    constexpr static_modint(T x) : static_modint((long long)x) {}
    template<std::unsigned_integral T>
    constexpr static_modint(T x) : static_modint((unsigned long long)x) {}
    
    using modint4724 = static_modint;
    constexpr modint4724 &operator+=(const modint4724 &p){
        _v += p._v;
        if (_v >= m) _v -= m;
        return *this;
    }
    constexpr modint4724 &operator-=(const modint4724 &p){
        _v += m - p._v;
        if (_v >= m) _v -= m;
        return *this;
    }
    constexpr modint4724 &operator*=(const modint4724 &p){
        unsigned long long a = _v, b = p._v;
        unsigned long long au = a >> 24, ad = a & MASK24;
        unsigned long long bu = b >> 24, bd = b & MASK24;
        unsigned long long X = (au + ad) * (bu + bd);
        unsigned long long Y = ad * bd;
        unsigned long long Z = au * bu;
        unsigned long long A = X - Y + Z, B = Y + m4 - 2*Z;
        unsigned long long Au = A >> 23, Ad = A & MASK23;
        _v = cal_mod(((Au + Ad) << 24) + B + m - Au);
        return *this;
    }
    constexpr modint4724 &operator/=(const modint4724 &p){
        *this *= p.inv();
        return *this;
    }
    friend constexpr modint4724 operator+(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) += rhs;
    }
    friend constexpr modint4724 operator-(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) -= rhs;
    }
    friend constexpr modint4724 operator*(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) *= rhs;
    }
    friend constexpr modint4724 operator/(const modint4724 &lhs, const modint4724 &rhs){
        return modint4724(lhs) /= rhs;
    }
    constexpr modint4724 operator+() const {
        return *this;
    }
    constexpr modint4724 operator-() const {
        return modint4724() - *this;
    }
    constexpr modint4724 inv() const {
        long long a = _v, b = m, u = 1, v = 0;
        while (b > 0){
            long long t = a / b;
            std::swap(a -= t * b, b);
            std::swap(u -= t * v, v);
        }
        return modint4724(u);
    }
    constexpr modint4724 pow(long long n) const {
        modint4724 ret(1ULL), mul(_v);
        while (n != 0){
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend std::istream &operator>>(std::istream &is, modint4724 &p){
        unsigned long long x;
        is >> x;
        p = modint4724(x);
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint4724 &p){
        return os << p._v;
    }
    constexpr unsigned long long val() const {
        return _v;
    }
    constexpr auto operator<=>(const modint4724 &) const = default;

  private:
    unsigned long long _v;
    static constexpr unsigned long long m = (1ULL << 47) - (1ULL << 24) + 1;
    static constexpr unsigned long long m4 = m << 2;
    static constexpr unsigned long long MASK23 = (1ULL << 23) - 1;
    static constexpr unsigned long long MASK24 = (1ULL << 24) - 1;
    static constexpr unsigned long long MASK47 = (1ULL << 47) - 1;
};
using modint4724 = static_modint<-4724>;

} // namespace noya2

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