#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll _ = 2e5 + 5;
ll N, n, k, l, r, z, t, a[_], b[_], i, j;
bool p(ll z) {
    t = k - z * n;
    for (i = 1; i <= n; i++) b[i] = a[i] - z;
    for (j = 0; j < 50; j++) {
        for (i = 1; i <= n; i++)
            if (b[i == n ? 1 : i + 1] & (1ll << j)) {
                b[i] -= ((1ll << j) << 1);
                b[i == n ? 1 : i + 1] += (1ll << j);
                t -= (1ll << j);
                if (t < 0)
                    return 0;
            }
    }
    return 1;
}
void P() {
    cin >> n;
    k = 0;
    for (i = 1; i <= n; i++) cin >> a[i], k += a[i];
    for (l = -1, r = k / n; l < r;) {
        z = (l + r + 1) >> 1;
        if (p(z))
            l = z;
        else
            r = z - 1;
    }
    cout << (l < 0 ? -1 : k - l * n) << '\n';
}
int main() {
    freopen("energy4.in", "r", stdin);
    freopen("energy4.ans", "w", stdout);
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cin >> N;
    while (N--) P();
}