#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl #define EACH(i, s) for (__typeof__((s).begin()) i = (s).begin(); i != (s).end(); ++i) template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template ostream& operator << (ostream &s, pair P) { return s << '<' << P.first << ", " << P.second << '>'; } template ostream& operator << (ostream &s, vector P) { for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; } template ostream& operator << (ostream &s, vector > P) { for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; } template ostream& operator << (ostream &s, map P) { EACH(it, P) { s << "<" << it->first << "->" << it->second << "> "; } return s << endl; } inline long long mod(long long a, long long m) { return (a % m + m) % m; } struct Fp { int MOD = 1000000007; long long val; Fp() : val(0) {} Fp(long long val_) { this->val = mod(val_, MOD); } Fp operator = (long long val_) { this->val = mod(val_, MOD); return *this; } inline Fp operator - () { return mod(-val, MOD); } inline const Fp& operator += (const Fp &x); inline const Fp& operator -= (const Fp &x); inline const Fp& operator *= (const Fp &x); inline const Fp& operator /= (const Fp &x); }; inline bool operator == (Fp x, Fp y) { return x.val == y.val; } inline bool operator != (Fp x, Fp y) { return !(x == y); } ostream &operator << (ostream &os, Fp x) { return os << x.val; } istream &operator >> (istream &is, Fp &x) { is >> x; return is; } inline Fp operator + (Fp x, Fp y) { return mod(x.val + y.val, x.MOD); } inline Fp operator - (Fp x, Fp y) { return mod(x.val - y.val, x.MOD); } inline Fp operator * (Fp x, Fp y) { return mod(x.val * y.val, x.MOD); } inline Fp operator / (Fp x, Fp y) { long long a = y.val, b = x.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 x * u; } inline Fp abs(Fp a) { return a; } inline Fp fpow(Fp a, long long n) { if (n == 0) return Fp(1); Fp t = fpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } inline const Fp& Fp::operator += (const Fp &x) { *this = *this + x; return *this; } inline const Fp& Fp::operator -= (const Fp &x) { *this = *this - x; return *this; } inline const Fp& Fp::operator *= (const Fp &x) { *this = *this * x; return *this; } inline const Fp& Fp::operator /= (const Fp &x) { *this = *this / x; return *this; } // calc comb (small n, r ver) const int FACT_MAX = 210000; static Fp fp_fact_val[FACT_MAX]; void calcFact(int MAX = FACT_MAX) { fp_fact_val[0] = 1; for (int val = 1; val < MAX; ++val) { fp_fact_val[val] = fp_fact_val[val - 1] * val; } } Fp fact(int n) { return fp_fact_val[n]; } Fp com(int n, int r) { return fact(n) / fact(r) / fact(n - r); } long long N; int K; //S(n, k) = sum((-1)^(k-i) com(k, i) i^n, i: 1~k) / k! int main() { calcFact(); while (cin >> N >> K) { Fp res = 0; for (int i = 1; i <= K; ++i) { Fp tmp = com(K, i) * fpow(i, N); if ((K - i) & 1) tmp = -tmp; res += tmp; } cout << res << endl; } }