#pragma GCC optimize "O3" #pragma GCC target "tune=native" #pragma GCC target "avx" #define NDEBUG 1 #include using namespace std; using ll = long long; constexpr ll MOD = 1000000007LL; constexpr int MAX = 10000; int K; ll ys[MAX + 2]; ll power(const ll p, const int n) { if (n == 0) { return 1; } if (n % 2 == 1) { return power(p, n - 1) * p % MOD; } else { const ll pp = power(p, n / 2); return pp * pp % MOD; } } inline ll inverse(const ll p) { return power(p, MOD - 2); } inline ll minu(const ll a, const ll b) { return (a >= b ? a - b : a + MOD - b); } inline ll LagrangeInterpolation(const ll x) { ll n = 1; for (ll i = 0; i <= K + 1; i++) { (n *= x - i) %= MOD; } ll ans = 0; for (ll i = 0; i <= K + 1; i++) { ll d = 1; for (ll j = 0; j <= K + 1; j++) { if (i == j) { continue; } (d *= minu(i, j)) %= MOD; } (ans += (n * inverse(x - i) % MOD) * (inverse(d) * ys[i] % MOD) % MOD) %= MOD; } return ans; } int main() { ll N; cin >> N >> K; N %= MOD; if (N == 0) { cout << 0 << endl; } else { for (int i = 1; i <= K + 1; i++) { ys[i] = (ys[i - 1] + power(i, K)) % MOD; if (i == N) { cout << ys[i] << endl; return 0; } } cout << LagrangeInterpolation(N) << endl; } return 0; }