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

int t;

long long choose(long long x) { //c(x, 3)
    if(x < 3)
        return 0;

    return (x * (x - 1) * (x - 2)) / 6;
}

long long h(long long p, long long x) { //c(p, 3) + c(p, 2) * (x - p)
    long long c1 = 0, c2 = 0;

    if(p >= 3)
        c1 = (p * (p - 1) * (p - 2)) / 6;

    if(p >= 2)
        c2 = (p * (p - 1)) / 2;
    c2 *= (x - p);

    return c1 + c2;
}


long long min_x(long long p, long long games) {
    long long lo = 0;
    long long hi = p;

    while(lo < hi) {
        long long mid = lo + (hi - lo) / 2;

        if(h(mid, p) >= games) {
            hi = mid;
        } else {
            lo = mid + 1;
        }
    }

    return lo;
}

bool check(long long p, long long total, long long max_games, vector<long long>& a) {
    long long possible = choose(p);

    if(possible < total || possible < max_games)
        return false;

    if(a.size() >= 2 && a[0] > 0 && a.back() > 0) {
        long long left = min_x(p, a[0]);
        long long right = min_x(p, a.back());

        if(left + right > p)
            return false;
    }

    return true;
}

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

    cin >> t;

    while(t--) {
        int n;
        cin >> n;

        vector<long long> a(n);
        long long total = 0, max_games = 0;

        for(int i = 0; i < n; i++) {
            cin >> a[i];
            total += a[i];
            max_games = max(max_games, a[i]);
        }

        long long lo = 3;
        long long hi = lo;

        while(!check(hi, total, max_games, a)) {
            hi *= 2;

            if(hi > LLONG_MAX)
                break;
        }

        long long ans = hi;

        while(lo <= hi) {
            long long mid = lo + (hi - lo) / 2;

            if(check(mid, total, max_games, a)) {
                ans = mid;
                hi = mid - 1;
            } else {
                lo = mid + 1;
            }
        }

        cout << ans << '\n';
    }
}