#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace atcoder;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define mod1 1000000007
#define mod2 998244353
#define mod3 100000007
#define vi vector<int>
#define vs vector<string>
#define vc vector<char>
#define vl vector<ll>
#define vb vector<bool>
#define vvi vector<vector<int>>
#define vvc vector<vector<char>>
#define vvl vector<vector<ll>>
#define vvb vector<vector<bool>>
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define pii pair<int, int>
#define pil pair<int, ll>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define vpii vector<pair<int, int>>
#define vpll vector<pair<ll, ll>>
#define vvpii vector<vector<pair<int, int>>>
#define vvpll vector<vector<pair<ll, ll>>>

template <typename T>
void debug(T e) {
    cerr << e << endl;
}

template <typename T>
void debug(vector<T> &v) {
    rep(i, v.size()) { cerr << v[i] << " "; }
    cerr << endl;
}

template <typename T>
void debug(vector<vector<T>> &v) {
    rep(i, v.size()) {
        rep(j, v[i].size()) { cerr << v[i][j] << " "; }
        cerr << endl;
    }
}

template <typename T>
void debug(vector<pair<T, T>> &v) {
    rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; }
}

template <typename T>
void debug(set<T> &st) {
    for (auto itr = st.begin(); itr != st.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(multiset<T> &ms) {
    for (auto itr = ms.begin(); itr != ms.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(map<T, T> &mp) {
    for (auto itr = mp.begin(); itr != mp.end(); itr++) {
        cerr << itr->first << " " << itr->second << endl;
    }
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << H << " ";
    debug_out(T...);
}

using mint = modint998244353;

void debug_mint1(vector<mint> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        cerr << vec[i].val() << " ";
    }
    cerr << endl;
}

void debug_mint2(vector<vector<mint>> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        for (int j = 0; j < vec[i].size(); j++) {
            cerr << vec[i][j].val() << " ";
        }
        cerr << endl;
    }
}

// 回数を持って dfs する。そのとき、top の要素がどれだけずれたかも情報として持つ
ll dfs(ll times, ll top, vector<ll> &vec, vector<ll> &true_seq){
    assert(times <= 200);
    ll len = vec.size();
    for (ll i = 0; i < len; i++){
        vec[i] -= times;
    }
    
    // まず先頭が 0 の場合を試す
    {
        bool all_same = true;
        for (ll i = 0; i < len; i++){
            if (vec[i] != true_seq[i]){
                all_same = false;
            }
        }
        if (all_same) return 0 - top;
    }
    // 先頭が 1 の場合を試す
    {
        bool all_same = true;
        for (ll i = 0; i < len; i++){
            if (vec[i] != true_seq[i + 1]){
                all_same = false;
            }
        }
        if (all_same) return 1 - top;
    }

    // そうでない場合は規則的
    // 長さが 2 の場合の答えを求めたい！
    {
        if (vec[0] <= 0 && vec[1] <= 0){
            return -1;
        }
        else if (vec[0] == 0){
            return ((1LL << vec[1]) - 1) * (1LL << times) - top;
        }
        else if (vec[0] == vec[1]){
            return ((1LL << (vec[0] + 1)) + 1) * (1LL << times) - top;
        }
        else if (vec[0] == vec[1] + 1){
            return (1LL << vec[0]) * (1LL << times) - top;
        }
        else if (vec[0] < vec[1]){
            return ((1LL << (vec[1] + 1)) + (1LL << (vec[1] - vec[0] + 1)) - 1) * (1LL << times) - top;
        }
        else return -1;
    }
    vector<ll> odd_vec;
    vector<ll> even_vec;
    even_vec.push_back(vec[0] + 1 + times);
    rep(i, len){
        if (i % 2 == 0) odd_vec.push_back(vec[i] + times);
        else even_vec.push_back(vec[i] + times);
    }
    bool pos_0 = true;
    for (ll i = 0; i < len; i += 2){
        if (i < len - 1){
            if (vec[i] != vec[i + 1] + 1){
                pos_0 = false;
            }
        }
    }
    if (pos_0){
        return dfs(times + 1, top, odd_vec, true_seq);
    }
    bool pos_1 = true;
    for (ll i = 1; i < len; i += 2){
        if (i < len - 1){
            if (vec[i] != vec[i + 1] + 1){
                pos_1 = false;
            }
        }
    }
    if (pos_1){
        return dfs(times + 1, top - (1LL << times), even_vec, true_seq);
    }
    return -1;
}

int main() {
    ll T;
    cin >> T;
    // 実際に数列を構成してしまう
    ll L = 1000004;
    vector<ll> true_seq(L, 0);
    for (ll i = 0; i < L; i++){
        ll top = -1;
        for (ll j = 0; j < 20; j++){
            if ((i >> j) & 1) top = j;
        }
        for (ll j = 0; j <= top; j++){
            if (!((i >> j) & 1)){
                true_seq[i]++;
            }
        }
    }
    true_seq[0]++;
    /*for (ll i = 0; i < 64; i++){
        cout << true_seq[i] << " ";
    }
    cout << endl;*/
    while (T--){
        // (1, 0, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, ...)
        // (1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, ...)
        // (1, 2, 3, 2, 4, 3, 3, 2, 5, 4, 4, 3, ...)
        // (1, 3, 4, 3, 5, 4, 4, 3, 6, 5, 5, 4, ...)
        // 先頭の要素を除いては 1 ずつ増えていっている！
        // つまり、何番目の再帰であるかを別で持っておけば答えられそう。
        ll N;
        cin >> N;
        vector<ll> A(N);
        rep(i, N) cin >> A[i];

        if (N == 1){
            if (A[0] == 1){
                cout << 0 << endl;
            }
            else{
                cout << (1LL << A[0]) << endl;
            }
        }
        else{
            ll ans = dfs(0, 0, A, true_seq);
            cout << ans << endl;
        }
    }   
}