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:heavy_check_mark: quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$ (modulus/mint_core.hpp)

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#pragma once
#include <cstdint>
#include <iostream>

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }

#line 2 "modulus/mint_core.hpp"
#include <cstdint>
#include <iostream>

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }

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