template <int mod>
struct ModInt {
int x;
ModInt(): x(0) {}
ModInt(int y): x(y >= 0 ? y : y + mod) {}
ModInt(ll y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
inline int inc(const int &v) {
return v >= mod ? v - mod : v;
}
inline int dec(const int &v) {
return v < 0 ? v + mod : v;
}
inline ModInt &operator+=(const ModInt &p) {
x = inc(x + p.x);
return *this;
}
inline ModInt &operator-=(const ModInt &p) {
x = dec(x - p.x);
return *this;
}
inline ModInt &operator*=(const ModInt &p) {
x = (int)((ll)x * p.x % mod);
return *this;
}
inline ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b, std::swap(a -= t * b, b), std::swap(u -= t * v, v);
}
return u;
}
inline ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
inline ModInt operator-() const {
return -x;
}
inline friend ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt(lhs) += rhs;
}
inline friend ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt(lhs) -= rhs;
}
inline friend ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt(lhs) *= rhs;
}
inline friend ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt(lhs) /= rhs;
}
inline bool operator==(const ModInt &p) const {
return x == p.x;
}
inline bool operator!=(const ModInt &p) const {
return x != p.x;
}
inline ModInt qpow(ll n) const {
ModInt ret(1), mul(x);
while (n > 0) {
if (n & 1) {
ret *= mul;
}
mul *= mul, n >>= 1;
}
return ret;
}
inline friend std::ostream &operator<<(std::ostream &os, const ModInt &p) {
return os << p.x;
}
inline friend std::istream &operator>>(std::istream &is, ModInt &a) {
ll t;
is >> t, a = ModInt<mod>(t);
return is;
}
static int get_mod() {
return mod;
}
inline bool operator<(const ModInt &A) const {
return x < A.x;
}
inline bool operator>(const ModInt &A) const {
return x > A.x;
}
};