/* * yuki/391/main.cpp */ // C++ 14 #include #include #include #include #include // memset #include using namespace std; #define ll long long #define loop(__x, __start, __end) for(int __x = __start; __x < __end; __x++) template ostream & operator << (ostream & out, vector const & v) { for (auto &&a: v) out << a << " "; out << endl; return out; } template void dump(T &a) { cout << a << endl; } template bool chmin(T &a, T b) { if (a > b) {a = b; return true; } return false; } template bool chmax(T &a, T b) { if (a < b) {a = b; return true; } return false; } /* Mod */ #define MOD 1000000007 struct mint { ll x; mint():x(0){} mint(ll x):x((x%MOD+MOD)%MOD){} // mint(ll x):x(x){} mint& fix() { x = (x%MOD+MOD)%MOD; return *this;} mint operator-() const { return mint(0) - *this;} mint& operator+=(const mint& a){ if((x+=a.x)>=MOD) x-=MOD; return *this;} mint& operator-=(const mint& a){ if((x+=MOD-a.x)>=MOD) x-=MOD; return *this;} mint& operator*=(const mint& a){ (x*=a.x)%=MOD; return *this;} mint operator+(const mint& a)const{ return mint(*this) += a;} mint operator-(const mint& a)const{ return mint(*this) -= a;} mint operator*(const mint& a)const{ return mint(*this) *= a;} bool operator<(const mint& a)const{ return x < a.x;} bool operator==(const mint& a)const{ return x == a.x;} }; ostream & operator << (ostream & out, mint const & v) { out << v.x; return out; } template T1 intpow(const T1& a, const T2 n) { if (n == 0) return 1; auto t = intpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } /* nCk */ template struct BiCoef { vector fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; /* * 区別ある人(玉)を区別ある問題(箱)に1人ずつ以上ずつ当てはめる問題. * sum((-1)^(k-1)*kCi*i^n | for i in [0, k]) */ ll N, M; BiCoef bc; void solve() { cin >> N >> M; if (N < M) { cout << 0 << endl; return; } bc.init(210000); mint sum = 0; for (ll i=0; i<=M; i++) { mint sign = 1; if ((M-i)%2 == 1) sign *= -1; sum += sign * bc.com(M, i) * intpow(mint(i), N); } cout << sum << endl; } int main() { // cout.precision(15); cout << fixed; solve(); return 0; }