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

using ll = long long;

ll take_two(ll n) {
    if (n < 2) return 0;
    return n * (n - 1) / 2;
}

ll take_three(ll n) {
    if (n < 3) return 0;
    return n * (n - 1) * (n - 2) / 6;
}

vector <ll> count(vector <ll> &v) {
    vector <ll> pref(v.size(), 0), suf(v.size(), 0);
    for (int i = 0; i < v.size(); i++) {
        if (i) pref[i] = pref[i - 1];
        pref[i] += v[i];
    }
    for (int i = (int)v.size() - 1; i >= 0; i--) {
        if (i != (int)v.size() - 1) suf[i] = suf[i + 1];
        suf[i] += v[i];
    }

    vector <ll> res(v.size());
    for (int i = 0; i < v.size(); i++) {
        res[i] = (i == 0 ? 0 : pref[i - 1]) * (i == (int)v.size() - 1 ? 0 : suf[i + 1]) * v[i];
        res[i] += take_two(v[i]) * (i == 0 ? 0 : pref[i - 1]);
        res[i] += take_two(v[i]) * (i == (int)v.size() - 1 ? 0 : suf[i + 1]);
        res[i] += take_three(v[i]);
    }
    return res;
}

void solve() {
    int n;
    cin >> n;
    vector <ll> v;
    for (int i = 0; i < n; i++) {
        ll a;
        cin >> a;
        if (a != 0) v.push_back(a);
    }

    n = (int)v.size();
    ll sum = accumulate(v.begin(), v.end(), 0LL);
    ll left = 1, right = 1e6, l = -1;
    while (left <= right) {
        ll mid = (left + right) / 2;
        if (take_three(mid) >= sum) {
            l = mid;
            right = mid - 1;
        } else left = mid + 1;
    }   

    auto check = [&](ll x) {
        ll pref = 0, S = x;
        for (int i = 0; i < n; i++) {
            ll l = 0, r = x, ans = -1;
            while (l <= r) {
                ll mid = (l + r) / 2;
                if (pref * mid * (S - pref - mid) + take_two(mid) * (S - mid) + take_three(mid) >= v[i]) {
                    ans = mid;
                    r = mid - 1;
                } else l = mid + 1;
            }
            if (ans == -1) return false;
            pref += ans;
            x -= ans;
        }
        return true;
    };

    ll r = 1e6, ans = -1;
    while (l <= r) {
        ll mid = (l + r) / 2;
        if (check(mid)) {
            ans = mid;
            r = mid - 1;
        } else l = mid + 1;
    }
    cout << ans << '\n';
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    int t;
    cin >> t;
    while (t--) solve();
}