#line 1 "/mnt/c/Users/leafc/dev/compro/lib/math/modint.hpp" #include #include #ifndef MOD_INT #define MOD_INT template class ModInt { using u64 = std::uint_fast64_t; public: ModInt(const u64 val = 0) { value = val % MOD; } ModInt operator+(const ModInt rhs) const { return ModInt(*this) += rhs; } ModInt operator-(const ModInt rhs) const { return ModInt(*this) -= rhs; } ModInt operator*(const ModInt rhs) const { return ModInt(*this) *= rhs; } ModInt operator/(const ModInt rhs) const { return ModInt(*this) /= rhs; } ModInt &operator+=(const ModInt rhs) { value += rhs.value; if (value >= MOD) { value -= MOD; } return *this; } ModInt &operator-=(const ModInt rhs) { if (value < rhs.value) { value += MOD; } value -= rhs.value; return *this; } ModInt &operator*=(const ModInt rhs) { value = value * rhs.value % MOD; return *this; } ModInt &operator/=(ModInt rhs) { *this *= rhs.inv(); return *this; } ModInt &operator++(int n) { value++; if (value >= MOD) { value -= MOD; } return *this; } ModInt &operator--(int n) { if (value == 0) { value += MOD; } value--; return *this; } ModInt inv() { return ModInt::pow(*this, MOD - 2); } static ModInt pow(ModInt base, long long int n) { ModInt res = ModInt(1); while (n) { if (n & 1) { res *= base; } base *= base; n /= 2; } return res; } static ModInt comb(ModInt n, ModInt r) { return comb(n.value, r.value); } static ModInt comb(int n, int r) { if (n < r) return ModInt(0); ModInt res = ModInt(1); for (int i = 0; i < r; i++) { res *= ModInt(n - i); } ModInt inv = ModInt(1); for (int i = 0; i < r; i++) { inv *= ModInt(r - i); } return res / inv; } u64 getValue() const { return value; } private: u64 value; friend std::ostream &operator<<(std::ostream &out, const ModInt &m) { out << m.value; return out; } friend std::istream &operator>>(std::istream &in, ModInt &m) { uint_fast64_t i; in >> i; m = ModInt(i); return in; } }; #endif #line 1 "/mnt/c/Users/leafc/dev/compro/lib/template.hpp" #include #define REP(i, n) for (int i = 0; i < n; i++) #define FOR(i, m, n) for (int i = m; i < n; i++) #define ALL(v) (v).begin(), (v).end() #define coutd(n) cout << fixed << setprecision(n) #define ll long long int #define vl vector #define vi vector #define MM << " " << using namespace std; template void say(bool val, T yes = "Yes", T no = "No") { cout << (val ? yes : no) << endl; } template void chmin(T &a, T b) { if (a > b) a = b; } template void chmax(T &a, T b) { if (a < b) a = b; } #line 3 "tmp.cpp" template std::vector combination_table(int n) { std::vector vec(n + 1); vec[0] = T(1); for (int r = 1; r < n + 1; r++) { vec[r] = vec[r - 1] * T(n - r + 1) / T(r); } return vec; } using mint = ModInt<(int)1e9 + 7>; int main() { cin.tie(0); ios::sync_with_stdio(false); int n, m; cin >> n >> m; auto ct = combination_table(m); vector dp(m + 1); dp[1] = mint(m); FOR(i, 2, m + 1) { mint tmp = ct[i] * mint::pow(mint(i), n) - dp[i - 1]; dp[i] = tmp; } cout << dp[m] << endl; return 0; }