Editorial for Robot

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The power of a robot is simply the multiplication of the prime numbers which can be extracted from the $N$ numbers. For each number, we can calculate all the primes which make that number.

Primes of $X$ can be calculated by iterating from 2 to the square root of $X$. For each iteration, it can be checked if $X$ can be divided by the number or not. If the number can be divided it's prime and if $X$ can be further divided to the number we divide till it cannot be divided. If the number cannot be divided by any numbers, then $X$ is a prime number and we insert it into our set. For example for a spell of power 18.

First check for 2. Since it can be divided by $X$ is 9 and we insert 2 into the set. 2 cannot divide 9. So we check for 2+1=3.
9 can be divided by 3 twice. 3 Will be inserted into the list and since $X$ is now 1, we can stop the process.

After all those numbers put in a set, we can simply take multiplication of all of them. (Not forgetting the modulo)

#include <bits/stdc++.h>
using namespace std;

const int md = (int) 1e9 + 7;
const int siz = 300005;

long long arr[siz];
long long n, m, k, l, x;
set<long long> s;

void addPrimes(long long x){
    int i=2;
    while(x!=1){
        while(x%i==0){
            x/=i;
            s.insert(i);
        }
        if(sqrt(x)<i) {
            s.insert(x);
            break;
        }
        i++;
    }
}

int main(){
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>x;
        addPrimes(x);
    }
    long long res=1;
    for(auto c:s){
        res*=c;
        res%=md;
    }
    cout<<res;
}