#include "bits/stdc++.h" // Begin Header {{{ using namespace std; #ifndef DEBUG #define dump(...) #endif #define all(x) x.begin(), x.end() #define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i) #define reps(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i) #define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i) #define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__) constexpr size_t operator""_zu(unsigned long long value) { return value; }; constexpr intmax_t operator""_jd(unsigned long long value) { return value; }; constexpr uintmax_t operator""_ju(unsigned long long value) { return value; }; constexpr int INF = 0x3f3f3f3f; constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd; template > using MaxHeap = priority_queue, Compare>; template > using MinHeap = priority_queue, Compare>; inline void input() {} template inline void input(Head&& head, Tail&&... tail) { cin >> head; input(forward(tail)...); } template inline istream& operator>>(istream &is, vector &vec) { for (auto &e: vec) { is >> e; } return is; } inline void output() { cout << "\n"; } template inline void output(Head&& head, Tail&&... tail) { cout << head; if (sizeof...(tail)) { cout << " "; } output(forward(tail)...); } template inline ostream& operator<<(ostream &os, const vector &vec) { static constexpr const char *delim[] = {" ", ""}; for (const auto &e: vec) { os << e << delim[&e == &vec.back()]; } return os; } template inline vector makeVector(const T &initValue, size_t sz) { return vector(sz, initValue); } template inline auto makeVector(const T &initValue, size_t sz, Args... args) { return vector(initValue, args...))>(sz, makeVector(initValue, args...)); } template class FixPoint : Func { public: explicit constexpr FixPoint(Func&& f) noexcept : Func(forward(f)) {} template constexpr decltype(auto) operator()(Args&&... args) const { return Func::operator()(*this, std::forward(args)...); } }; template static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept { return FixPoint{forward(f)}; } template struct reverse_t { Container &c; reverse_t(Container &c) : c(c) {} auto begin() { return c.rbegin(); } auto end() { return c.rend(); } }; template auto reversed(Container &c) { return reverse_t(c); } template inline bool chmax(T &a, const T &b) noexcept { return b > a && (a = b, true); } template inline bool chmin(T &a, const T &b) noexcept { return b < a && (a = b, true); } template inline T diff(const T &a, const T &b) noexcept { return a < b ? b - a : a - b; } // End Header }}} const intmax_t MOD = intmax_t(1e9) + 7; // ModInt {{{ template class ModInt { intmax_t value; public: inline ModInt(const ModInt& other) : value(other.value) {} inline ModInt(intmax_t value = 0) { if (value >= MOD) { this->value = value % MOD; } else if (value < 0) { this->value = (value + MOD) % MOD; } else { this->value = value; } } template explicit inline operator T() const { return static_cast(value); } inline ModInt inverse() const { return ModInt::pow(value, MOD - 2); } inline ModInt& operator+=(const ModInt other) { value = (value + other.value) % MOD; return *this; } inline ModInt& operator-=(const ModInt other) { value = (MOD + value - other.value) % MOD; return *this; } inline ModInt& operator*=(const ModInt other) { value = (value * other.value) % MOD; return *this; } inline ModInt& operator/=(const ModInt other) { value = (value * other.inverse().value) % MOD; return *this; } inline ModInt operator+(const ModInt other) { return ModInt(*this) += other; } inline ModInt operator-(const ModInt other) { return ModInt(*this) -= other; } inline ModInt operator*(const ModInt other) { return ModInt(*this) *= other; } inline ModInt operator/(const ModInt other) { return ModInt(*this) /= other; } inline bool operator==(const ModInt other) { return value == other.value; } inline bool operator!=(const ModInt other) { return value != other.value; } friend ostream& operator<<(ostream &os, const ModInt other) { os << other.value; return os; } friend istream& operator>>(istream &is, ModInt& other) { is >> other.value; return is; } static constexpr inline ModInt pow(intmax_t n, intmax_t p) { intmax_t ret = 1; for (; p > 0; p >>= 1) { if (p & 1) ret = (ret * n) % MOD; n = (n * n) % MOD; } return ret; } }; using Mint = ModInt; // }}} // Factorial {{{ #ifdef DEBUG #define constexpr #endif template struct Factorial { vector fact_; constexpr inline Factorial() : fact_(N + 1) { fact_[0] = 1; for (intmax_t i = 1; i <= N; ++i) { fact_[i] = (fact_[i - 1] * i) % MOD; } } constexpr inline Mint operator[](size_t pos) const { return fact_[pos]; } }; template struct InvFact { vector inv_; vector finv_; constexpr inline InvFact() : inv_(N + 1), finv_(N + 1) { inv_[1] = 1; finv_[0] = finv_[1] = 1; for (intmax_t i = 2; i <= N; ++i) { inv_[i] = (MOD - MOD / i) * inv_[MOD % i] % MOD; finv_[i] = finv_[i - 1] * inv_[i] % MOD; } } constexpr inline Mint operator[](size_t pos) const { return finv_[pos]; } }; #ifdef constexpr #undef constexpr #endif Factorial<510000, MOD> fact; InvFact<510000, MOD> finv; inline Mint nCr(int n, int r) { if (r < 0 || n < r) { return 0; } return fact[n] * (finv[r] * finv[n - r]); } inline Mint nPr(int n, int r) { if (r < 0 || n < r) { return 0; } return fact[n] * finv[n - r]; } inline Mint nHr(int n, int r) { return nCr(n + r - 1, r); } // }}} signed main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.setf(ios_base::fixed); cout.precision(10); var(intmax_t, N, M); Mint res = Mint::pow(M, N); Mint u = 0; rep(i, 1, M) { const Mint val = nCr(M, i) * Mint::pow(i, N); if (i & 1) u += val; else u -= val; } output(res - u); return 0; }