牛客寒假算法训练1 D 欧拉（容斥）

 1 #include<bits/stdc++.h>
 using namespace std;
 const int maxn=;
 typedef long long ll;
 int p[maxn],a[maxn];
     ll n,k,A,B;
 const int mod=1e9+;

 ll Pow(ll x,ll n)
 {
     ll res=;
     while(n>)
     {
        if(n%==)
        {
          res=res*x;
          res=res%mod;
        }
        x=x*x;
        x=x%mod;
        n>>=;
     }
     return res;
 }
     long long z,sum=;
     ll flag=;
 ll cal(ll n=){
     ll res=;
     for(ll i=;i<(<<flag);i++){
         ll t=i,tmp=,k=;
         ll len=;
         while(t){
             if(t&){
                 tmp*=a[k];
                 len++;
             }
             t>>=;
             k++;
         }
         //cout<<tmp<<"fuck"<<endl;
         if(len&) res+=(tmp+n/tmp*tmp)*n/tmp/;//等差数列和
         else res-=(tmp+n/tmp*tmp)*n/tmp/;
         res%=mod-;
     }
     return res;
 }

 int main(){

 cin>>n>>k>>A>>B;
 sum=;
  z=n;
  flag=;
     for(ll i=;i<=n;){
         if(n%i==){
             while(n%i==){
                 p[i]++;
                 n/=i;
             }
             a[flag++]=i;
         }
         if(i==)i++;
         else i+=;
     }
    sum=cal(z);
   // cout<<sum<<endl;
     long long x=(z)*(z+)/;
     x-=sum;
     x%=mod-;
     long long ans=(A+B)%mod*Pow(k,x%(mod-)+mod-)%mod;
     cout<<ans<<endl;
     return ;
 }