暑假集训Day1 B(拓展欧拉定理)

 这题公式其实非常好推，主要是在幂的指数上取模的时候，应该用欧拉定理，指数上模的应该是MOD对应的欧拉函数值

#include "bits/stdc++.h"
using namespace std;
typedef long long LL;
const int MOD=1e9+7;
const int MAX=2e5+5;
LL ans,n,a[MAX],b[MAX],c[MAX];
LL ksm(LL x,LL y){
    LL an=1ll;
    while (y){
        if (y%2==1ll) an=(an*x)%MOD;
        x=(x*x)%MOD;
        y/=2ll;
    }
    return an;
}
LL ksm2(LL x,LL y){
    LL an=1ll;
    while (y){
        if (y%2==1ll) an=(an*x)%(MOD-1);
        x=(x*x)%(MOD-1);
        y/=2ll;
    }
    return an;
}
inline LL read(){
    LL an(0ll),x=1ll;char c=getchar();
    while (c<'0' || c>'9') {if (c=='-') x=-1;c=getchar();}
    while (c>='0' && c<='9') {an=an*10+c-'0';c=getchar();}
    return an*x;
}
bool cmp(LL x,LL y){
    return x<y;
}
int main(){
    freopen ("b.in","r",stdin);
    freopen ("b.out","w",stdout);
    int i,j;
    LL x,y,z,mul=1ll;
    n=read();
    for (i=1;i<=n;i++) a[i]=read();
    sort(a+1,a+n+1,cmp);
    memset(b,0,sizeof(b));
    memset(c,0,sizeof(c));
    for (i=1;i<=n;i++)
        if (a[i]!=a[i-1]){
            b[++b[0]]=a[i];
            c[++c[0]]=1;
        }
        else c[c[0]]++;
    ans=1ll;bool flag=true;
    for (i=1;i<=c[0];i++){
        mul=(mul*(c[i]+1))%(MOD-1);
        if ((c[i]+1)%2==0 && flag){
            flag=false;
            mul/=2;
        }
    }
    for (i=1;i<=b[0];i++){
        x=c[i];
        if (flag) x/=2ll;
        z=(x*mul%(MOD-1))%(MOD-1);
        ans=(ans*ksm(b[i],z))%MOD;
    }
    printf("%lld",ans);
    return 0;
}