#include using namespace std; typedef long long signed int LL; typedef long long unsigned int LU; #define incID(i, l, r) for(int i = (l) ; i < (r); i++) #define incII(i, l, r) for(int i = (l) ; i <= (r); i++) #define decID(i, l, r) for(int i = (r) - 1; i >= (l); i--) #define decII(i, l, r) for(int i = (r) ; i >= (l); i--) #define inc(i, n) incID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec(i, n) decID(i, 0, n) #define dec1(i, n) decII(i, 1, n) #define inII(v, l, r) ((l) <= (v) && (v) <= (r)) #define inID(v, l, r) ((l) <= (v) && (v) < (r)) #define PB push_back #define EB emplace_back #define MP make_pair #define FI first #define SE second #define PQ priority_queue #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define FOR(it, v) for(auto it = v.begin(); it != v.end(); ++it) #define RFOR(it, v) for(auto it = v.rbegin(); it != v.rend(); ++it) template bool setmin(T & a, T b) { if(b < a) { a = b; return true; } else { return false; } } template bool setmax(T & a, T b) { if(b > a) { a = b; return true; } else { return false; } } template bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } } template bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } } template T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); } template T lcm(T a, T b) { return a / gcd(a, b) * b; } // ---- ---- LL MOD; LL mod(LL x, LL m = MOD) { return (x % m + m) % m; } pair ex_gcd(LL a, LL b) { if(b == 0) { return MP(1, 0); } auto p = ex_gcd(b, a % b); return MP(p.SE, p.FI - (a / b) * p.SE); } LL inv(LL x, LL m = MOD) { assert(gcd(x, m) == 1); auto p = ex_gcd(x, m); return mod(p.FI, m); } LL promod(LL x, LL y, LL m = MOD) { return mod((x % m) * (y % m), m); } LL divmod(LL x, LL y, LL m = MOD) { return promod(x, inv(y, m), m); } // ---- struct CombMod { LL lim = 0, mod; LL * fact; // fact[i]: i の階乗 LL * finv; // finv[i]: i の階乗の逆元 CombMod() { } CombMod(LL lim, LL mod = MOD) { init(lim, mod); } void init(LL arg_lim, LL arg_mod = MOD) { lim = arg_lim; mod = arg_mod; fact = new LL[lim + 1]; finv = new LL[lim + 1]; fact[0] = 1; inc1(i, lim) { fact[i] = promod(fact[i - 1], i, mod); } finv[lim] = inv(fact[lim], mod); dec(i, lim) { finv[i] = promod(finv[i + 1], i + 1, mod); } } LL P(LL a, LL b) { assert(inII(a, 0, lim) && inII(b, 0, lim)); return (a < b ? 0 : promod(fact[a], finv[a - b], mod)); } LL C(LL a, LL b) { assert(inII(a, 0, lim) && inII(b, 0, lim)); return (a < b ? 0 : promod(P(a, b), finv[b], mod)); } LL H(LL a, LL b) { assert(inII(a, 0, lim) && inII(b, 0, lim) && inII(a + b - 1, -1, lim)); return (a == 0 ? (b == 0) : C(a + b - 1, b)); } }; // ---- LL ex(LL x, LL y, LL mod = MOD) { LL z[64], v = 1; inc(i, 64) { z[i] = (i == 0 ? x : z[i - 1] * z[i - 1]) % mod; } inc(i, 64) { if((y >> i) & 1) { (v *= z[i]) %= mod; } } return v; } // ---- const int LIM = 10000; LL B[LIM + 2]; CombMod cm; void calc_bernoulli_number_mod(LL n, LL m, int sgn = -1) { // calc: [0, n], m: prime number // sgn == -1: B- (B(1) == -1/2) // sgn == +1: B+ (B(1) == +1/2) assert(abs(sgn) == 1); incII(i, 0, n) { if(i == 0) { B[0] = 1; } else { B[i] = 0; inc(k, i) { (B[i] += cm.C(i + 1, k) * B[k]) %= m; } // ここが遅すぎて TLE B[i] = divmod(-B[i], i + 1, m); } } if(sgn == +1) { B[1] = divmod(+1, 2, m); } } LL sum_power(LL n, LL k, LL m) { // (1^k + 2^k + ... + n^k) % m assert(k <= LIM); cm.init(k + 1, m); calc_bernoulli_number_mod(k, m, +1); LL ans = 0; incII(i, 0, k) { (ans += cm.C(k + 1, i) * B[i] % m * ex(n, k + 1 - i, m)) %= m; } return divmod(ans, k + 1, m); } int main() { LL n, k; cin >> n >> k; cout << sum_power(n, k, 1e9 + 7) << endl; return 0; }