modInt

#include <iostream>

template<int mod> struct ModInt{
    int x;
    ModInt () : x(0) {}
    ModInt (int64_t x) : x(x >= 0 ? x % mod : (mod - -x % mod) % mod) {}
    ModInt &operator += (const ModInt &p){
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator -= (const ModInt &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator *= (const ModInt &p) {
        x = (int64_t) x * p.x % mod;
        return *this;
    }
    ModInt &operator /= (const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }
    ModInt &operator ^= (int64_t p) {
        ModInt res = 1;
        for (; p; p >>= 1) {
            if (p & 1) res *= *this;
            *this *= *this;
        }
        return *this = res;
    }
    ModInt operator - () const { return ModInt(-x); }
    ModInt operator + (const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator - (const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator * (const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator / (const ModInt &p) const { return ModInt(*this) /= p; }
    ModInt operator ^ (int64_t p) const { return ModInt(*this) ^= p; }
    bool operator == (const ModInt &p) const { return x == p.x; }
    bool operator != (const ModInt &p) const { return x != p.x; }
    explicit operator int() const { return x; }
    ModInt &operator = (const int p) { x = p; return *this;}
    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            a -= t * b;
            std::swap(a, b);
            u -= t * v;
            std::swap(u, v);
        }
        return ModInt(u);
    }
    friend std::ostream & operator << (std::ostream &stream, const ModInt<mod> &p) {
        return stream << p.x;
    }
    friend std::istream & operator >> (std::istream &stream, ModInt<mod> &a) {
        int64_t x;
        stream >> x;
        a = ModInt<mod>(x);
        return stream;
    }
};

int main() {

    return 0;
}