#include #include #include #include #include #include #include #include #include #include #include #include #include #define INF 1000000000ll #define MOD 1000000007ll #define EPS 1e-10 #define REP(i,m) for(long long i=0; i P; typedef long double ld; ll _pow(ll a, ll n) { if(n==0) return 1; else { ll res = 1; ll buf = a; while(n>0) { if(n%2==1) { res *= buf; res %= MOD; } buf *= buf; buf %= MOD; n/=2; } return res; } } #define MAX_N 1000000 long long extgcd(long long a, long long b, long long& x, long long& y) { long long d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } long long mod_inverse(long long a, long long m) { long long x, y; if(extgcd(a, m, x, y) == 1) return (m + x % m) % m; else return -1; } vector fact(MAX_N+1, INF); long long mod_fact(long long n, long long& e) { if(fact[0] == INF) { fact[0]=1; if(MAX_N != 0) fact[1]=1; for(ll i = 2; i <= MAX_N; ++i) { fact[i] = (fact[i-1] * i) % MOD; } } e = 0; if(n == 0) return 1; long long res = mod_fact(n / MOD, e); e += n / MOD; if((n / MOD) % 2 != 0) return (res * (MOD - fact[n % MOD])) % MOD; return (res * fact[n % MOD]) % MOD; } // return nCk long long mod_comb(long long n, long long k) { if(n < 0 || k < 0 || n < k) return 0; long long e1, e2, e3; long long a1 = mod_fact(n, e1), a2 = mod_fact(k, e2), a3 = mod_fact(n - k, e3); if(e1 > e2 + e3) return 0; return (a1 * mod_inverse((a2 * a3) % MOD, MOD)) % MOD; } int main() { cin.tie(0); ios::sync_with_stdio(false); ll n,k; cin>>n>>k; n%=MOD; vector ber(k+2,0); ber[0]=1; FOR(i,1,k+2) { REP(j,i) { if(j%2==i%2) ber[i]-=mod_comb(i+1,j)*ber[j]; else ber[i]+=mod_comb(i+1,j)*ber[j]; } ber[i]/=i+1; } ld ans=0; REP(i,k+2) { ans+=(_pow(n,(k+1)-i)*mod_comb(k+1,i))%MOD*ber[i]; ans=round(ans); } ans-=ber[k+1]; ll tmp=round(ans); tmp*=_pow(k+1,MOD-2); tmp=(tmp%MOD+MOD)%MOD; cout<