#include #include #include #include #include #include #include using namespace std; typedef long long ll; const int mod = 1000000007; // assert mod is prime template struct Mint { int x; Mint() : x(0) {} Mint(int y) : x(y >= 0 ? y % M : M - (-y) % M) {} Mint &operator += (const Mint &rhs) { if((x += rhs.x) >= M) x -= M; return *this; } Mint &operator -= (const Mint &rhs) { if((x += M - rhs.x) >= M) x -= M; return *this; } Mint &operator *= (const Mint &rhs) { x = 1LL * x*rhs.x % M; return *this; } Mint &operator /= (const Mint &rhs) { x = (1LL * x*rhs.inv().x) % M; return *this; } Mint operator - () const { return Mint(-x); } Mint operator + (const Mint &rhs) const { return Mint(*this) += rhs; } Mint operator - (const Mint &rhs) const { return Mint(*this) -= rhs; } Mint operator * (const Mint &rhs) const { return Mint(*this) *= rhs; } Mint operator / (const Mint &rhs) const { return Mint(*this) /= rhs; } bool operator < (const Mint &rhs) const { return x < rhs.x; } Mint inv() const { signed a = x, b = M, u = 1, v = 0, t; while(b) { t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } return Mint(u); } Mint pow(long long t) const { Mint e = *this, res = 1; for(; t; e *= e, t >>= 1) if(t & 1) res *= e; return res; } }; template ostream &operator << (ostream &os, const Mint &rhs) { return os << rhs.x; } template istream &operator >> (istream &is, Mint &rhs) { long long s; is >> s; rhs = Mint(s); return is; }; using mint = Mint; ll modpow(ll x, ll y, ll m) { if(y == 0) return 1; ll res = modpow(x, y / 2, m); return res * res % m * (y & 1 ? x : 1) % m; } ll modinv(ll x, ll m) { return modpow(x, m - 2, m); } struct Comb { int sz; vector mfact, mfinv; Comb(int N) : sz(min(N, int(mod) - 1)), mfact(sz + 1), mfinv(sz + 1) { for(int i = 0; i <= sz; i++) mfact[i] = (i == 0 ? 1 : mfact[i - 1] * i); mfinv[sz] = mfact[sz].inv(); for(int i = sz; i >= 1; i--) mfinv[i - 1] = mfinv[i] * i; } mint fact(int n, int& e) { // e に p の指数が入る // Wilson の定理 e = 0; if(n <= sz) return mfact[n]; mint res = fact(n / mod, e); e += n / mod; if(n / mod % 2 != 0) return -res * mfact[n % mod]; return res * mfact[n % mod]; } mint nPr(int n, int r) { int e; return fact(n, e) / fact(n - r, e); } mint nCr(int n, int r) { // Lucus の定理 assert(n <= sz); if(n >= mod) return nCr(n%mod, r%mod) * nCr(n / mod, r / mod); return r > n ? 0 : mfact[n] * mfinv[n - r] * mfinv[r]; } mint nHr(int n, int r) { return r == 0 ? 1 : nCr(n + r - 1, r); } }; int main() { cin.tie(0); ios::sync_with_stdio(false); ll N, M; cin >> N >> M; if(M > N) { cout << 0 << endl; return 0; } Comb C(1000000); mint ans = mint(M).pow(N); for(int i = 1; i < M; i++) { mint m = mint(M - i).pow(N); m *= C.nCr(M, i); if(i % 2) ans -= m; else ans += m; } cout << ans << endl; }