#include #include #include #include using namespace std; typedef long long ll; map, ll> cmb; int64_t ans; const int64_t MOD = 1e9+7; void add(int64_t& a, int64_t b){ a = (a+b) % MOD; } void mul(int64_t& a, int64_t b){ a = a*b % MOD; } vector fact, seq_inv, fact_inv; void create_fact_mod(int num){ fact[0] = fact[1] = 1; for(int i=2; i<=num; i++) fact[i] = fact[i-1] * i % MOD; } void create_seq_inv_mod(int num){ seq_inv[0] = seq_inv[1] = 1; for(int i=2; i<=num; i++) seq_inv[i] = (MOD - MOD/i) * seq_inv[MOD%i] % MOD; } void create_fact_inv_mod(int num){ fact_inv[0] = fact_inv[1] = 1; for(int i=2; i<=num; i++) fact_inv[i] = fact_inv[i-1] * seq_inv[i] % MOD; } void create_mod_tables(int num){ fact.resize(num+1); seq_inv.resize(num+1); fact_inv.resize(num+1); create_fact_mod(num); create_seq_inv_mod(num); create_fact_inv_mod(num); } int64_t comb_mod(int n, int k){ return fact[n] * fact_inv[n-k] % MOD * fact_inv[k] % MOD; } int64_t perm_mod(int n, int k){ return fact[n] * fact_inv[n-k] % MOD; } int64_t power_mod(int64_t num, int64_t power){ int64_t prod = 1; num %= MOD; while(power > 0){ if(power&1) prod = prod * num % MOD; num = num * num % MOD; power >>= 1; } return prod; } int64_t extgcd(int64_t a, int64_t b, int64_t& x, int64_t& y){ int64_t d = a; if(b != 0){ d = extgcd(b, a%b, y, x); y -= (a/b) * x; }else{ x = 1; y = 0; } return d; } int64_t inv_mod(int64_t a){ int64_t x, y; extgcd(a, MOD, x, y); return (MOD + x%MOD) % MOD; } int main() { int n, m; cin >> n >> m; ans = power_mod(m, n); create_mod_tables(200000); int k = -1; for (int j = 1; j < m; ++j) { int64_t xs = 1; mul(xs, k); add(xs, MOD); mul(xs, power_mod(j, n)); add(xs, MOD); mul(xs, comb_mod(m, j)); add(xs, MOD); add(ans, xs); add(ans, MOD); k *= -1; } cout << ans << endl; return 0; }