#include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef long long ll; typedef vector vl; typedef vector> vvl; typedef pair P; #define rep(i, n) for(ll i = 0; i < n; i++) #define exrep(i, a, b) for(ll i = a; i <= b; i++) #define out(x) cout << x << endl #define exout(x) printf("%.10f\n", x) #define chmax(x, y) x = max(x, y) #define chmin(x, y) x = min(x, y) #define all(a) a.begin(), a.end() #define rall(a) a.rbegin(), a.rend() #define pb push_back #define re0 return 0 const ll mod = 1000000007; const ll INF = 1e16; const ll MAX_N = 200010; // aのn乗を求める。計算量はO(logn) ll modpow(ll a, ll n) { if(n == 0) { return 1; } if(n%2 == 1) { return (a * modpow(a, n-1))%mod; } return (modpow(a, n/2) * modpow(a, n/2))%mod; } ll inverse(ll a) { return modpow(a, mod-2); } ll inv[MAX_N]; // inv[i] : iの逆数のmod ll fact[MAX_N]; // fact[i] : iの階乗のmod ll invfact[MAX_N]; void init() { inv[0] = fact[0] = invfact[0] = 1; inv[1] = 1; for(ll i = 1; i < MAX_N; i++) { if(i >= 2) { inv[i] = mod - inv[mod%i]*(mod/i)%mod; } fact[i] = (i*fact[i-1])%mod; invfact[i] = inverse(fact[i]); } } ll Comb(ll n, ll r) { if(r < 0 || n < 0 || n < r) { return 0; } ll res = fact[n]; res = (res * invfact[r])%mod; res = (res * invfact[n-r])%mod; return res; } //--- main関数でinit()を呼び出すのを忘れるな ---// int main() { ll n, m; cin >> n >> m; init(); ll x = 0; ll y = 0; ll cnt = 0; for(ll i = m; i >= 1; i--) { ll a = Comb(m, i); ll b = modpow(i, n); if(cnt%2 == 0) { x += (a*b)%mod; x %= mod; } else { y += (a*b)%mod; y %= mod; } cnt++; } ll ans = (x + mod - y)%mod; out(ans); re0; }