正题

题目链接:https://www.luogu.org/problemnew/show/P2842

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题目大意

求
$a\#b=a^{a^{a^{a^{{\dots }^a}}}}($进行幂运算b次)

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解题思路

根据费马小当p为质数时
$$a^p\equiv a(modp)$$
推导得$$a^b\equiv a^{b\%(p-1)}(modp)$$
所以答案$$a\#b\equiv a^{a^{b-1}\%(p-1)}(modp)$$

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$code$

#include<cstdio>
#include<algorithm>
#define ll long long
using namespace std;
const ll XJQ=1e9+7;
ll a,b;
ll power(ll a,ll b,ll p)
{ll ans=1;a%=p;while(b){if(b&1) ans=ans*a%p;a=a*a%p;b>>=1;}return ans;
}
int main()
{scanf("%lld%lld",&a,&b);ll k=power(a,b-1,XJQ-1);printf("%lld",power(a,k,XJQ));
}