Codeforces 776E The Holmes Children

题目链接：http://codeforces.com/problemset/problem/776/E

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${\because gcd(i,n-i)=1\Leftrightarrow gcd(i,n)=1}$

${\therefore f(x)=\phi (x)}$

${\because \sum_{d|x}\phi(d)=x}$

${\therefore g(x)=x}$

问题转换为求${\phi(\phi(\phi(...)))}$嵌套${\left \lfloor \frac{k}{2} \right \rfloor}$层。

考虑这样的嵌套至多${log}$次就会到$1$，所以直接暴力做就可以了。

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 #include<iostream>
 #include<cstdio>
 #include<algorithm>
 #include<vector>
 #include<cstdlib>
 #include<cmath>
 #include<cstring>
 using namespace std;
 #define maxn 10010
 #define llg long long
 #define md 1000000007
 #define yyj(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);

 llg phi(llg x)
 {
     llg m=sqrt(x+0.5);
     llg ans=x;
     for (llg i=;i<=m;i++)
         if (x%i==)
         {
             ans=ans/i*(i-);
             while (x%i==) x/=i;
         }
     if (x>) ans=ans/x*(x-);
     return ans;
 }
 llg n,m,k;

 int main()
 {
     yyj("E");
     cin>>n>>k;
     llg ans=phi(n);
     for (llg i=;i<=k;i++)
     {
         if (i%) ans=phi(ans);
         if (ans==phi(ans)) break;
     }
     cout<<ans%md;
     return ;
 }