#include "bits/stdc++.h" using namespace std; #define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i)) #define rep(i,j) FOR(i,0,j) #define each(x,y) for(auto &(x):(y)) #define mp make_pair #define all(x) (x).begin(),(x).end() #define debug(x) cout<<#x<<": "<<(x)< pii; typedef vector vi; typedef vector vll; template class ModInt{ public: ModInt():value(0){} ModInt(int val):value(val<0?MOD+val%MOD:val%MOD){ } ModInt& operator+=(ModInt that){ value = value+that.value; if(value>=MOD)value-=MOD; return *this; } ModInt& operator-=(ModInt that){ value -= that.value; if(value<0)value+=MOD; return *this; } ModInt& operator*=(ModInt that){ value = (int)((long long)value * that.value % MOD); return *this; } ModInt &operator/=(ModInt that){ return *this *= that.inverse(); } ModInt operator+(ModInt that) const{ return ModInt(*this)+=that; } ModInt operator-(ModInt that) const{ return ModInt(*this)-=that; } ModInt operator*(ModInt that) const{ return ModInt(*this)*=that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt operator^(long long k) const{ ModInt n = *this, res = 1; while(k){ if(k & 1)res *= n; n *= n; k >>= 1; } return res; } ModInt inverse() const { long long a = value, b = MOD, u = 1, v = 0; while(b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } return ModInt(u); } int toi() const{ return value; } private: int value; }; typedef ModInt<1000000007> mint; ostream& operator<<(ostream& os, const mint& x){ os << x.toi(); return os; } // n以下の階乗を返す template vector factorials(int n){ vector res(n + 1); res[0] = res[1] = 1; for(int i = 2; i <= n; ++i) res[i] = res[i - 1] * i; return res; } mint nCr(int n, int r, const vector &fact){ return fact[n] / (fact[r] * fact[n - r]); } /* |A|>=|B|を満たす空でない集合A,Bについて |A|=n, |B|=kとおく。 このとき、f:A->B であるようなすべての全射関数を数える。 O(klog(n)) 検証済み */ mint countSurjectiveFunctions(long long n, int k, const vector &fact){ mint res = 0; for(int i = 1; i <= k; ++i){ mint d = nCr(k, i, fact); d *= (mint(i)^n); if((k - i) % 2)d *= -1; res += d; } return res; } ll N; int M; int main(){ while(cin >> N >> M){ if(M > N){ puts("0"); continue; } auto f = factorials(M); mint ans = countSurjectiveFunctions(N, M, f); cout << ans << endl; } }