Codeforces 776E The Holmes Children

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

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

${ herefore f(x)=phi (x)}$

${ecause sum_{d|x}phi(d)=x}$

${ herefore g(x)=x}$

问题转换为求${phi(phi(phi(...)))}$嵌套${left lfloor frac{k}{2} ight floor}$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=2;i<=m;i++)
        if (x%i==0)
        {
            ans=ans/i*(i-1);
            while (x%i==0) x/=i;
        }
    if (x>1) ans=ans/x*(x-1);
    return ans;
}
llg n,m,k;

int main()
{
    yyj("E");
    cin>>n>>k;
    llg ans=phi(n);
    for (llg i=2;i<=k;i++)
    {
        if (i%2) ans=phi(ans);
        if (ans==phi(ans)) break;
    }
    cout<<ans%md;
    return 0;
}