import bisect import copy import decimal import fractions import functools import heapq import itertools import math import random import sys from collections import Counter,deque,defaultdict from functools import lru_cache,reduce from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max def _heappush_max(heap,item): heap.append(item) heapq._siftdown_max(heap, 0, len(heap)-1) def _heappushpop_max(heap, item): if heap and item < heap[0]: item, heap[0] = heap[0], item heapq._siftup_max(heap, 0) return item from math import gcd as GCD read=sys.stdin.read readline=sys.stdin.readline readlines=sys.stdin.readlines def Comb(N,K,mod=0): if K<0 or K>N: return 0 K=min(K,N-K) s=1 if mod: for i in range(N,N-K,-1): s*=i s%=mod ss=1 for i in range(1,K+1): ss*=i ss%=mod s*=MOD(mod).Pow(ss,-1) s%=mod else: for i in range(N-K+1,N+1): s*=i for i in range(1,K+1): s//=i return s def Bernoulli_Numbers(N,mod=0): bernoulli_numbers=[0]*(N+1) if mod else [fractions.Fraction(0)]*(N+1) bernoulli_numbers[0]+=1 if mod: MD=MOD(mod) MD.Build_Fact(N+1) for i in range(1,N+1): bernoulli_numbers[i]=-MD.Pow(i+1,-1)*sum(MD.Comb(i+1,j)*bernoulli_numbers[j] for j in range(i))%mod else: for i in range(1,N+1): bernoulli_numbers[i]=-sum(Comb(i+1,j)*bernoulli_numbers[j] for j in range(i))/(i+1) return bernoulli_numbers class Faulhaber: def __init__(self,K,mod=0): self.K=K self.mod=mod if self.mod: bernoulli_numbers=Bernoulli_Numbers(self.K,self.mod) MD=MOD(self.mod) MD.Build_Fact(self.K+1) inve=MD.Pow(self.K+1,-1) self.coefficient=[bernoulli_numbers[i]*MD.Comb(self.K+1,i)*inve%mod for i in range(self.K+1)] for i in range(1,self.K+1,2): self.coefficient[i]*=-1 self.coefficient[i]%=mod else: bernoulli_numbers=Bernoulli_Numbers(self.K) self.coefficient=[bernoulli_numbers[i]*Comb(self.K+1,i)/(K+1) for i in range(self.K+1)] for i in range(1,self.K+1,2): self.coefficient[i]*=-1 def __call__(self,N): retu=0 N_pow=N for i in range(self.K+1): retu+=N_pow*self.coefficient[self.K-i] N_pow*=N if self.mod: retu%=self.mod N_pow%=self.mod return retu def Extended_Euclid(n,m): stack=[] while m: stack.append((n,m)) n,m=m,n%m if n>=0: x,y=1,0 else: x,y=-1,0 for i in range(len(stack)-1,-1,-1): n,m=stack[i] x,y=y,x-(n//m)*y return x,y class MOD: def __init__(self,p,e=1): self.p=p self.e=e self.mod=self.p**self.e def Pow(self,a,n): a%=self.mod if n>=0: return pow(a,n,self.mod) else: assert math.gcd(a,self.mod)==1 x=Extended_Euclid(a,self.mod)[0] return pow(x,-n,self.mod) def Build_Fact(self,N): assert N>=0 self.factorial=[1] self.cnt=[0]*(N+1) for i in range(1,N+1): ii=i self.cnt[i]=self.cnt[i-1] while ii%self.p==0: ii//=self.p self.cnt[i]+=1 self.factorial.append((self.factorial[-1]*ii)%self.mod) self.factorial_inve=[None]*(N+1) self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1) for i in range(N-1,-1,-1): ii=i+1 while ii%self.p==0: ii//=self.p self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod def Fact(self,N): return self.factorial[N]*pow(self.p,self.cnt[N],self.mod)%self.mod def Fact_Inve(self,N): if self.cnt[N]: return None return self.factorial_inve[N] def Comb(self,N,K,divisible_count=False): if K<0 or K>N: return 0 retu=self.factorial[N]*self.factorial_inve[K]*self.factorial_inve[N-K]%self.mod cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K] if divisible_count: return retu,cnt else: retu*=pow(self.p,cnt,self.mod) retu%=self.mod return retu N,K=map(int,readline().split()) F=Faulhaber(K) ans=F(N) print(ans)