iiitv/ChefLib

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// ~~~~~~~© Aashutosh Rathi~~~~~~
// ~~~~~~~~aashutosh001~~~~~~~~~~
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

// Answer Status : Wrong Answer

#include <bits/stdc++.h>
#include <stdio.h>

using namespace std;

#define mod(x)            x%1000000007;
#define MIN(n1, n2 )    ((n1) > (n2) ? (n2) : (n1))
#define MAX(n1, n2 )    ((n1) > (n2) ? (n1) : (n2))
#define MID(s, e)        (s+(e-s)/2)
#define FOR(i, a, b)    int i; for(i=(a);i<(b);i++)
#define FORD(i, a, b)    int i; for(i=(a);i>(b);i--)
#define show(a)            for(i=0;i<sizeof(a);i++) cout<<a[i]<<" ";
#define get(a)            for(i=0;i<sizeof(a);i++) cin>>a[i];
#define scanint(a)        scanf("%d",&a)
#define scanLLD(a)        scanf("%lld",&a)
#define scanstr(s)        scanf("%s",s)
#define scanline(l)     scanf(" %[^\n]",l);

typedef long int BIG;
typedef unsigned long long PAPA;

long long fast_power(long long base, long long power) {
    long long result = 1;
    while(power > 0) {

        if(power % 2 == 1) { // Can also use (power & 1) to make code even faster
            result = (result*base);
        }
        base = (base * base);
        power = power / 2; // Can also use power >>= 1; to make code even faster
    }
    return result;
}

bool check(PAPA pro, int n) {
    PAPA val = round(pow(pro, 1.0/n));
    if(val == pow(pro, 1.0/n)) {
        return true;
    }
    return false;
}


int main() {
    std::ios_base::sync_with_stdio(false);
    int n, i;
    cin >> n;
    long a[n];
    PAPA pro = 1, res = 1;
    for(i = 0; i < n; i++) {
        cin >> a[i];
        pro = (pro * a[i]);
    }
    PAPA val = round(pow(pro, 1.0/n));
    if(check(pro, n)) {
        cout << "justdoit";
    }
    else {
        PAPA pro2 = pro;

        long c[(long)sqrt(pro)+1];
        bool b[(long)sqrt(pro)+1];

        memset(c, 0, sqrt(pro)+1);
        memset(b, false, sqrt(pro)+1);

        i=2;
        while(pro2%i == 0) {
                b[i] = true;
                c[i]++;
                pro2 = pro2/i;
            }

        for(i=3; i<=sqrt(pro); i=i+2) {
            while(pro2%i == 0) {
                b[i] = true;
                c[i]++;
                pro2 = pro2/i;
            }
        }

        for(i=2; i<=sqrt(pro); i++) {
            if(b[i]) {
                //cout << i <<" : "<<c[i] << " ";
                long x;
                if(c[i]%(n+1) == 0) {
                    x = 0;
                }
                else {
                    x = ((c[i]/(n+1))+1)*(n+1)-c[i];
                }
                res = res * fast_power(i, x);
            }
        }
        cout << mod(res);
    }

    return 0;
}