#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; typedef long long ll; typedef vector vl; typedef vector> vvl; typedef pair P; #define rep(i, n) for(ll i = 0; i < n; i++) #define exrep(i, a, b) for(ll i = a; i <= b; i++) #define out(x) cout << x << endl #define exout(x) printf("%.10f\n", x) #define chmax(x, y) x = max(x, y) #define chmin(x, y) x = min(x, y) #define all(a) a.begin(), a.end() #define rall(a) a.rbegin(), a.rend() #define pb push_back #define re0 return 0 const ll mod = 1000000007; const ll INF = 1e16; const ll MAX = 20010; ll fact[MAX]; // fact[i] : iの階乗のmod ll inv[MAX]; // inv[i] : iの逆数のmod ll invfact[MAX]; // invfact[i] : iの階乗の逆数のmod void init() { fact[0] = 1; inv[0] = inv[1] = 1; invfact[0] = 1; for(ll i = 1; i < MAX; i++) { fact[i] = i * fact[i-1] % mod; if(i >= 2) { inv[i] = mod - inv[mod % i] * (mod / i) % mod; } invfact[i] = invfact[i-1] * inv[i] % mod; } } // nCrをO(n)で求める。 ll Comb(ll n, ll r) { if(r < 0 || n < 0 || n < r) { return 0; } ll res = fact[n]; res = (res * invfact[r]) % mod; res = (res * invfact[n - r]) % mod; return res; } int main() { ll n, k; cin >> n >> k; init(); vl B(k+1); // B[i] : i番目のベルヌーイ数 B[0] = 1; exrep(i, 1, k) { rep(j, i) { B[i] += Comb(i+1, j) * B[j]; B[i] %= mod; } B[i] = B[i] * (mod - inv[i+1]) % mod; } vl vec(k+2); // vec[i] : n^i vec[0] = 1; exrep(i, 1, k+1) { vec[i] = vec[i-1] * (n % mod) % mod; } ll S_k = 0; // Σ i^k (1 <= i <= n) exrep(i, 0, k) { S_k += Comb(k+1, i) * B[i] % mod * vec[k + 1 - i]; S_k %= mod; } S_k = S_k * inv[k+1] % mod; out(S_k); re0; }