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template <i64 mod = MOD> struct ModInt{ i64 p; ModInt() : p(0){} ModInt(i64 x){p = x >= 0 ? x % mod : x + (-x + mod - 1) / mod * mod;} ModInt& operator+=(const ModInt& y){p = p + *y - ((p + *y) >= mod ? mod : 0); return *this;} ModInt& operator-=(const ModInt& y){p = p - *y + (p - *y < 0 ? mod : 0); return *this;} ModInt& operator*=(const ModInt& y){p = (p * *y) % mod; return *this;} ModInt& operator%=(const ModInt& y){if(y)p %= *y; return *this;} ModInt operator+(const ModInt& y) const{ModInt x = *this; return x += y;} ModInt operator-(const ModInt& y) const{ModInt x = *this; return x -= y;} ModInt operator*(const ModInt& y) const{ModInt x = *this; return x *= y;} ModInt operator%(const ModInt& y) const{ModInt x = *this; return x %= y;} friend ostream& operator<<(ostream& stream, const ModInt<mod>& x){ stream << *x; return stream; } friend ostream& operator>>(ostream& stream, const ModInt<mod>& x){ stream >> *x; return stream; } ModInt& operator++(){p = (p + 1) % mod; return *this;} ModInt& operator--(){p = (p - 1 + mod) % mod; return *this;} bool operator==(const ModInt& y) const{return p == *y;} bool operator!=(const ModInt& y) const{return p != *y;} const i64& operator*() const{return p;} i64& operator*(){return p;} }; using mint = ModInt<>;
#line 1 "lib/classes/modint.cpp" template <i64 mod = MOD> struct ModInt{ i64 p; ModInt() : p(0){} ModInt(i64 x){p = x >= 0 ? x % mod : x + (-x + mod - 1) / mod * mod;} ModInt& operator+=(const ModInt& y){p = p + *y - ((p + *y) >= mod ? mod : 0); return *this;} ModInt& operator-=(const ModInt& y){p = p - *y + (p - *y < 0 ? mod : 0); return *this;} ModInt& operator*=(const ModInt& y){p = (p * *y) % mod; return *this;} ModInt& operator%=(const ModInt& y){if(y)p %= *y; return *this;} ModInt operator+(const ModInt& y) const{ModInt x = *this; return x += y;} ModInt operator-(const ModInt& y) const{ModInt x = *this; return x -= y;} ModInt operator*(const ModInt& y) const{ModInt x = *this; return x *= y;} ModInt operator%(const ModInt& y) const{ModInt x = *this; return x %= y;} friend ostream& operator<<(ostream& stream, const ModInt<mod>& x){ stream << *x; return stream; } friend ostream& operator>>(ostream& stream, const ModInt<mod>& x){ stream >> *x; return stream; } ModInt& operator++(){p = (p + 1) % mod; return *this;} ModInt& operator--(){p = (p - 1 + mod) % mod; return *this;} bool operator==(const ModInt& y) const{return p == *y;} bool operator!=(const ModInt& y) const{return p != *y;} const i64& operator*() const{return p;} i64& operator*(){return p;} }; using mint = ModInt<>;