// https://github.com/potato167/po167_library
#include <bits/stdc++.h>
#include <cassert>
using namespace std;
using ll=long long;
const ll ILL=2167167167167167167;
const int INF=2100000000;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using pq_ = priority_queue<T, vector<T>, greater<T>>;
template<class T> int LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> int UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,T b){if(b<a){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
template<class T> void vec_out(vector<T> &p,int ty=0){
    if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
    else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(int)(a&1),a>>=1;}return res;}
template<class T> T square(T a){return a * a;}



void solve();
// DEAR MYSTERIES / TOMOO
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t = 1;
    cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    int N;
    cin >> N;
    vector<int> A(N);
    rep(i, 0, N) cin >> A[i];
    auto f = [&](ll a) -> int {
        if (a == 0) return 1;
        int res = 0;
        while (a) {
            if (a % 2 == 0) res++;
            a /= 2;
        }
        return res;
    };
    if (A[0] == 1) {
        int ok = 1;
        rep(i, 1, N) {
            if (A[i] != f(i)) {
                ok = 0;
            }
        }
        if (ok) {
            cout << "0\n";
            return;
        }
    }
    if (N == 1) {
        cout << (1ll << A[0]) << "\n";
        return;
    }
    if (N == 2 && A[0] > A[1]) {
        if (A[0] - A[1] != 1) {
            cout << "-1\n";
            return;
        }
        cout << (1ll << A[0]) << "\n";
        return;
    }
    int dif = -1;
    int a = -1;
    rep(i, 0, N - 1) {
        if (chmax(dif, A[i + 1] - A[i])) {
            a = i;
        }
    }
    if (a == -1) {
        cout << "-1\n";
        return;
    }
    auto ch = [&](ll L) -> int {
        rep(i, 0, N) if (A[i] != f(L + i)) return 0;
        return 1;
    };
    if (A[a] == 0) {
        ll L = (1ll << A[a + 1]) - a - 1;
        if (ch(L)) cout << L << "\n";
        else cout << "-1\n";
    }
    else {
        ll D = A[a] + dif + 1;
        ll tmp = (1ll << (dif + 1)) - 1;
        tmp += (1ll << D);
        while (tmp <= a) {
            D++;
            tmp += (1ll << D);
        }
        ll L = tmp - a;
        if (ch(L)) cout << L << "\n";
        else cout << "-1\n";
    }
}
// 流石に初回のACPC Cと同じでいいか？
// f(0) = 1 <- やばすぎ
// 差分の一番大きいところを見るが、そこが初回か否かで話は少し違う
// A[a] != 1 のとき
// 1000101111
// 1 + 0 * A[a] + 1 * (dif + 1) とか？