#include #define rep(i,a,b) for(int i=a;i=b;i--) #define fore(i,a) for(auto &i:a) #define all(x) (x).begin(),(x).end() #pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b v; vector fac, inv, finv; void init(int _n, int mo = 1000000007) { n = _n; mod = mo; fac.resize(n + 1); fac[0] = 1; rep(i, 1, n + 1) fac[i] = (1LL * fac[i - 1] * i) % mod; inv.resize(n + 1); inv[1] = 1; rep(i, 2, n + 1) inv[i] = (1LL * inv[mod % i] * (mod - mod / i)) % mod; finv.resize(n + 1); finv[0] = 1; rep(i, 1, n + 1) finv[i] = (1LL * finv[i - 1] * inv[i]) % mod; } int modpow(int x, int n) { int res = 1; while (n) { if (n & 1) res = (1LL * res * x) % mod; x = (1LL * x * x) % mod; n >>= 1; } return res; } int modinv(int a) { return modpow(a, mod - 2); } void add(int y) { v.push_back(y); } int get(ll x) { if (x <= n) return v[x]; assert(n + 1 <= v.size()); int num = 1; rep(i, 0, n + 1) num = (1LL * num * ((x - i) % mod)) % mod; int res = 0; rep(i, 0, n + 1) { int d = (1LL * v[i] * num) % mod; d = (1LL * d * modinv((x - i) % mod)) % mod; d = (1LL * d * finv[i]) % mod; d = (1LL * d * finv[n-i]) % mod; if ((n - i) & 1) d = mod - d; res = (res + d) % mod; } return res; } // for 1^k + 2^k + ... + n^k (mod10^9+7) void initexpsum(int k, int mo = 1000000007) { assert(k <= 2000000); init(k + 1, mo); int sm = 0; rep(i, 0, k + 2) { sm = (sm + modpow(i, k)) % mod; add(sm); } } }; /*---------------------------------------------------------------------------------------------------             ∧_∧       ∧_∧  (´<_` )  Welcome to My Coding Space!      ( ´_ゝ`) /  ⌒i     /   \    | |     /   / ̄ ̄ ̄ ̄/  |   __(__ニつ/  _/ .| .|____      \/____/ (u ⊃ ---------------------------------------------------------------------------------------------------*/ LagrangePolynomial lp; ll N, K; //--------------------------------------------------------------------------------------------------- void _main() { cin >> N >> K; lp.initexpsum(K); cout << lp.get(N) << endl; }