#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <list>
using namespace std;
using ll = long long;
ll gcd(ll a, ll b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}
int T = 0;
void EachT()
{
    T++;
    cout << "Case " << T << ": ";
    int n;
    cin >> n;
    vector<ll> a(n), div(n);
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
    }
    sort(a.begin(), a.end());
    ll total = 0;
    for (int i = 1; i < n; i++)
    {
        div[i] = a[i] - a[i - 1];
        // cout<<div[i]<<' ';
        total = gcd(total, div[i]);
        // cout<<total<<'\n';
    }
    if (total == 0)
    {
        if (a[n - 1] == 1)
        {
            cout << 1 << '\n';
            return;
        }
        cout << 0 << '\n';
        return;
    }
    if (total == 1)
    {
        cout << "-1" << '\n';
    }
    else
    {
        ll ans = 1e10;
        for (int i = 2; i * i <= total; i++)
        {
            if (total % i == 0)
            {
                ll fac = i;
                if (a[0] % fac == 0)
                {
                    ans = 0;
                }
                else
                {
                    ans = min(ans, fac - a[0] % fac);
                }
                fac = total / i;
                if (a[0] % fac == 0)
                {
                    ans = 0;
                }
                else
                {
                    ans = min(ans, fac - a[0] % fac);
                }
            }
        }
        ll fac = total;
        if (a[0] % fac == 0)
        {
            ans = 0;
        }
        else
        {
            ans = min(ans, fac - a[0] % fac);
        }
        cout << ans << '\n';
    }
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int t;
    cin >> t;
    while (t--)
    {
        EachT();
    }
    return 0;
}