#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; } } // f(i) = y_i (0 <= i <= n) を満たすn次多項式fの f(t) (mod.MOD) の値をO(n)で求める。 ll Lagrange_interpolation(const vl& y, ll t, ll MOD = mod) { ll n = y.size() - 1; if(t <= n) { return y[t] % MOD; } init(); vl dp(n+1, 1), pd(n+1, 1); rep(i, n) { dp[i+1] = (t - i) % MOD * dp[i] % MOD; } for(ll i = n; i >= 1; i--) { pd[i-1] = (t - i) % MOD * pd[i] % MOD; } ll res = 0; exrep(i, 0, n) { ll tmp = y[i] % MOD * dp[i] % MOD * pd[i] % MOD * invfact[i] % MOD * invfact[n - i] % MOD; if((n - i) & 1) { res += MOD - tmp; } else { res += tmp; } res %= MOD; } return res; } // a^n (mod.MOD)を求める。計算量はO(logn) ll modpow(ll a, ll n, ll MOD = mod) { if(n == 0) { return 1; } if(n % 2 == 1) { return a * modpow(a, n-1, MOD) % MOD; } return modpow(a, n/2, MOD) * modpow(a, n/2, MOD) % MOD; } int main() { ll n, k; cin >> n >> k; vl a(k+2); exrep(i, 1, k+1) { a[i] = a[i-1] + modpow(i, k); a[i] %= mod; } out(Lagrange_interpolation(a, n)); re0; }