jiangly's Mint模板

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template<class T>
constexpr T power(T a, i64 b) {
    T res = 1;
    for (; b; b /= 2, a *= a) {
        if (b % 2) {
            res *= a;
        }
    }
    return res;
}

template<int P>
struct MInt {
    int x;

    constexpr MInt() : x{} {}

    constexpr MInt(i64 x) : x{norm(x % P)} {}

    constexpr int norm(int x) const {
        if (x < 0) {
            x += P;
        }
        if (x >= P) {
            x -= P;
        }
        return x;
    }

    constexpr int val() const {
        return x;
    }

    explicit constexpr operator int() const {
        return x;
    }

    constexpr MInt operator-() const {
        MInt res;
        res.x = norm(P - x);
        return res;
    }

    constexpr MInt inv() const {
        assert(x != 0);
        return power(*this, P - 2);
    }

    constexpr MInt &operator*=(MInt rhs) {
        x = 1LL * x * rhs.x % P;
        return *this;
    }

    constexpr MInt &operator+=(MInt rhs) {
        x = norm(x + rhs.x);
        return *this;
    }

    constexpr MInt &operator-=(MInt rhs) {
        x = norm(x - rhs.x);
        return *this;
    }

    constexpr MInt &operator/=(MInt rhs) {
        return *this *= rhs.inv();
    }

    friend constexpr MInt operator*(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res *= rhs;
        return res;
    }

    friend constexpr MInt operator+(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res += rhs;
        return res;
    }

    friend constexpr MInt operator-(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res -= rhs;
        return res;
    }

    friend constexpr MInt operator/(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res /= rhs;
        return res;
    }

    friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
        i64 v;
        is >> v;
        a = MInt(v);
        return is;
    }

    friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
        return os << a.val();
    }

    friend constexpr bool operator==(MInt lhs, MInt rhs) {
        return lhs.val() == rhs.val();
    }

    friend constexpr bool operator!=(MInt lhs, MInt rhs) {
        return lhs.val() != rhs.val();
    }
};

template<int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();

constexpr int P = 998244353;
using Z = MInt<P>;

struct Combinatorics {
    int n;
    std::vector<Z> _fac;
    std::vector<Z> _invfac;
    std::vector<Z> _inv;

    Combinatorics() : n{0}, _fac{1}, _invfac{1}, _inv{0} {}

    Combinatorics(int n) : Combinatorics() {
        init(n);
    }

    void init(int m) {
        if (m <= n) return;
        _fac.resize(m + 1);
        _invfac.resize(m + 1);
        _inv.resize(m + 1);

        for (int i = n + 1; i <= m; i++) {
            _fac[i] = _fac[i - 1] * i;
        }
        _invfac[m] = _fac[m].inv();
        for (int i = m; i > n; i--) {
            _invfac[i - 1] = _invfac[i] * i;
            _inv[i] = _invfac[i] * _fac[i - 1];
        }
        n = m;
    }

    Z fac(int m) {
        if (m > n) init(2 * m);
        return _fac[m];
    }

    Z invfac(int m) {
        if (m > n) init(2 * m);
        return _invfac[m];
    }

    Z inv(int m) {
        if (m > n) init(2 * m);
        return _inv[m];
    }

    // fac 是阶乘(n!)
    // invfac是除阶乘(1 / n!)
    Z binom(int n, int m) {
        if (n < m || m < 0) return 0;
        return fac(n) * invfac(m) * invfac(n - m);
    }
} combinatorics;