[Luogu5106]dkw的lcm

https://minamoto.blog.luogu.org/solution-p5106

容易想到枚举质因子及其次数计算其贡献，容斥计算$\varphi(p^i)$的次方数。

 #include<cstdio>
 #include<algorithm>
 #define rep(i,l,r) for (int i=(l); i<=(r); i++)
 typedef long long ll;
 using namespace std;

 const int N=,mod=1e9+;
 int n,k,tot,ans,b[N],p[N];

 int ksm(int a,int b,int mod){
     int res=;
     for (; b; a=1ll*a*a%mod,b>>=)
         if (b & ) res=1ll*res*a%mod;
     return res;
 }

 void init(){
     rep(i,,n){
         if (!b[i]) p[++tot]=i;
         for (int j=; j<=tot && i*p[j]<=n; j++){
             b[i*p[j]]=;
             if (i%p[j]==) break;
         }
     }
 }

 int D(ll pi,ll pi1){
     int s1=ksm(n-n/pi,k,mod-),s2=ksm(n-n/pi1,k,mod-);
     return (s1-s2+mod-)%(mod-);
 }

 int main(){
     scanf("%d%d",&n,&k); init(); ans=;
     rep(i,,tot)
         for (ll t=p[i]; t<=n; t*=p[i])
             ans=1ll*ans*ksm(t-t/p[i],D(t*p[i],t),mod)%mod;
     printf("%d\n",ans);
     return ;
 }