http://codeforces.com/contest/1165/problem/D
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a[2000200],f,t,n,l,r,ans;
int main() {
scanf("%lld", &t);
while (t--) {
scanf("%lld", &n);
for (int i = 1; i <= n; i++) {
scanf("%lld", &a[i]);
}
sort(a + 1, a + n + 1);
l = 1;
r = n;
f = 1;
ans = a[1] * a[n];
for (ll i = 2; i * i <= ans; i++) {
if (ans % i == 0) {
if (a[l] != i || a[r] != ans / i) {
f = 0;
} else {
l++;
r--;
}
}
}
if (l <= r) {
f = 0;
}
if (f) {
printf("%lld\n", ans);
} else {
printf("-1\n");
}
}
}