Modulo Integer

overflow에 안전한 int 자료형

struct mint {
    int val;
    mint() { val = 0; }
    mint(const ll& v) {
        val = (-MOD <= v && v < MOD) ? v : v % MOD;
        if (val < 0) val += MOD;
    }

    friend ostream& operator<<(ostream& os, const mint& a) { return os << a.val; }
    friend bool operator==(const mint& a, const mint& b) { return a.val == b.val; }
    friend bool operator!=(const mint& a, const mint& b) { return !(a == b); }
    friend bool operator<(const mint& a, const mint& b) { return a.val < b.val; }

    mint operator-() const { return mint(-val); }
    mint& operator+=(const mint& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; }
    mint& operator-=(const mint& m) { if ((val -= m.val) < 0) val += MOD; return *this; }
    mint& operator*=(const mint& m) { val = (ll)val*m.val%MOD; return *this; }
    friend mint ipow(mint a, ll p) {
        mint ans = 1; for (; p; p /= 2, a *= a) if (p&1) ans *= a;
        return ans;
    }
    friend mint inv(const mint& a) { assert(a.val); return ipow(a, MOD - 2); }
    mint& operator/=(const mint& m) { return (*this) *= inv(m); }

    friend mint operator+(mint a, const mint& b) { return a += b; }
    friend mint operator-(mint a, const mint& b) { return a -= b; }
    friend mint operator*(mint a, const mint& b) { return a *= b; }
    friend mint operator/(mint a, const mint& b) { return a /= b; }
    operator int64_t() const { return val; }
};