#include #include #include #include #include template inline bool chmin(T &lhs, const U &rhs) { if (lhs > rhs) { lhs = rhs; return true; } return false; } template inline bool chmax(T &lhs, const U &rhs) { if (lhs < rhs) { lhs = rhs; return true; } return false; } // [l, r) from l to r struct range { struct itr { int i; constexpr itr(int i_): i(i_) { } constexpr void operator ++ () { ++i; } constexpr int operator * () const { return i; } constexpr bool operator != (itr x) const { return i != x.i; } }; const itr l, r; constexpr range(int l_, int r_): l(l_), r(std::max(l_, r_)) { } constexpr itr begin() const { return l; } constexpr itr end() const { return r; } }; // [l, r) from r to l struct revrange { struct itr { int i; constexpr itr(int i_): i(i_) { } constexpr void operator ++ () { --i; } constexpr int operator * () const { return i; } constexpr bool operator != (itr x) const { return i != x.i; } }; const itr l, r; constexpr revrange(int l_, int r_): l(l_ - 1), r(std::max(l_, r_) - 1) { } constexpr itr begin() const { return r; } constexpr itr end() const { return l; } }; template class modulo_int { public: static constexpr int mod = T::value; static_assert(mod > 0, "mod must be positive"); private: long long value; constexpr void normalize() { value %= mod; if (value < 0) value += mod; } public: constexpr modulo_int(long long value_ = 0): value(value_) { normalize(); } constexpr modulo_int operator - () const { return modulo_int(mod - value); } constexpr modulo_int operator ~ () const { return power(mod - 2); } constexpr long long operator () () const { return value; } constexpr modulo_int operator + (const modulo_int &rhs) const { return modulo_int(*this) += rhs; } constexpr modulo_int &operator += (const modulo_int &rhs) { if ((value += rhs.value) >= mod) value -= mod; return (*this); } constexpr modulo_int operator - (const modulo_int &rhs) const { return modulo_int(*this) -= rhs; } constexpr modulo_int &operator -= (const modulo_int &rhs) { if ((value += mod - rhs.value) >= mod) value -= mod; return (*this); } constexpr modulo_int operator * (const modulo_int &rhs) const { return modulo_int(*this) *= rhs; } constexpr modulo_int &operator *= (const modulo_int &rhs) { (value *= rhs.value) %= mod; return (*this); } constexpr modulo_int operator / (const modulo_int &rhs) const { return modulo_int(*this) /= rhs; } constexpr modulo_int &operator /= (const modulo_int &rhs) { return (*this) *= ~rhs; } constexpr bool operator == (const modulo_int &rhs) const { return value == rhs(); } constexpr bool operator != (const modulo_int &rhs) const { return value != rhs(); } constexpr modulo_int power (unsigned long long pow) const { modulo_int result(1), mult(*this); while (pow > 0) { if (pow & 1) result *= mult; mult *= mult; pow >>= 1; } return result; } friend std::istream &operator >> (std::istream &stream, modulo_int &lhs) { stream >> lhs.value; lhs.normalize(); return stream; } friend std::ostream &operator << (std::ostream &stream, const modulo_int &rhs) { return stream << rhs.value; } }; template class factorials { public: using value_type = T; public: std::vector fact, fact_inv; factorials(int size_ = 200000): fact(size_ + 1), fact_inv(size_ + 1) { fact[0] = 1; for (int i = 1; i <= size_; ++i) { fact[i] = fact[i - 1] * value_type(i); } fact_inv[size_] = ~fact[size_]; for (int i = size_; i > 0; --i) { fact_inv[i - 1] = fact_inv[i] * value_type(i); } } value_type operator () (int n, int r) const { return fact[n] * fact_inv[n - r] * fact_inv[r]; } }; using modint = modulo_int>; factorials fact(100000); int main() { int N, M; std::cin >> N >> M; modint ans = modint(M).power(N); for (int i: range(1, M)) { if (i % 2 == 1) { ans -= fact(M, i) * modint(M - i).power(N); } else { ans += fact(M, i) * modint(M - i).power(N); } } std::cout << ans << '\n'; return 0; }