#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef long long ll; typedef pair P; typedef bitset<16> BS; struct edge { int to, cost, id; }; const ll MOD = 1E+09 + 7; // =998244353; const ll INF = 1E18; const int MAX_N = 1E+05; ll dx[4] = { -1, 1, 0, 0 }, dy[4] = { 0, 0, -1, 1 }; ll N, M; ll modfac[MAX_N + 1]; ll modfacinv[MAX_N + 1]; ll modPow(ll x, ll a); ll modfactor(ll p); void modfactorInv(ll n); int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cin >> N >> M; modfactor(M); ll ans = 0; for (ll i = 0; i <= M; i++) { ll res = ((modfac[M] * modfacinv[M - i]) % MOD * modfacinv[i]) % MOD; res *= modPow(M - i, N); res %= MOD; if (i & 1) { ans += (-res + MOD) % MOD; ans %= MOD; } else { ans += res; ans %= MOD; } } /* for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { cout << "i = " << i << ", j = " << j << ", dp = " << dp[i][j] << "\n"; } } */ cout << ans << "\n"; return 0; } // n!を求める ll modfactor(ll n) { modfac[0] = 1; ll p = 1; while (p <= n) { //cout << p << "\n"; modfac[p] = (p * modfac[p - 1]) % MOD; p++; } modfacinv[n] = modPow(modfac[n], MOD - 2); modfactorInv(n); return modfac[n]; } // (n!)^-1を求める void modfactorInv(ll n) { ll p = n - 1; while (p >= 0) { modfacinv[p] = ((p + 1) * modfacinv[p + 1]) % MOD; p--; } } ll modPow(ll x, ll a) { ll ans = 1; while (a > 0) { if (a & 1) { ans = (ans * x) % MOD; } x = (x * x) % MOD; a >>= 1; } return ans; }