#include #include #include using namespace std; long power(long base, int exponent){ if(exponent % 2){ return power(base, exponent - 1) * base % long(1e9 + 7); }else if(exponent){ long root_ans = power(base, exponent / 2); return root_ans * root_ans % long(1e9 + 7); }else{ return 1; } } vector factorial{1}; vector factorial_inverse_element{1}; long combination(int n, int r){ return factorial[n] * factorial_inverse_element[r] % long(1e9 + 7) * factorial_inverse_element[n - r] % long(1e9 + 7); } int main(){ long n; int k; cin >> n >> k; for(long i = 1; i < 1e5; i++){ factorial.push_back(factorial.back() * i % long(1e9 + 7)); factorial_inverse_element.push_back(power(factorial.back(), 1e9 + 5)); } long bernoulli_numbers[k + 1]; bernoulli_numbers[0] = 1; for(int i = 1; i <= k; i++){ bernoulli_numbers[i] = 0; for(int j = 0; j < i; j++){ if(j % 2){ bernoulli_numbers[i] += bernoulli_numbers[j] * combination(i + 1, j) % long(1e9 + 7); }else{ bernoulli_numbers[i] += long(1e9 + 7) - bernoulli_numbers[j] * combination(i + 1, j) % long(1e9 + 7); } } bernoulli_numbers[i] %= long(1e9 + 7); if(i % 2){ bernoulli_numbers[i] *= long(1e9 + 7) - power(combination(i + 1, i), 1e9 + 5); }else{ bernoulli_numbers[i] *= power(combination(i + 1, i), 1e9 + 5); } bernoulli_numbers[i] %= long(1e9 + 7); } long ans = 0; for(int i = 0; i <= k; i++){ ans += combination(k + 1, i) * bernoulli_numbers[i] % long(1e9 + 7) * power(n % long(1e9 + 7), k + 1 - i) % long(1e9 + 7); } cout << ans % long(1e9 + 7) * power(k + 1, 1e9 + 5) % long(1e9 + 7) << endl; }