#include <bits/stdc++.h>
#define FOR(i,a,b) for (int i = (a); i < (b); i++)
using namespace std;
using ll=long long;
//上
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int t; cin >> t;
    while(t--){
        ll n; cin >> n;
        vector<ll> v(n);
        FOR(i,0,n) cin >> v[i];
        if(n == 1){
            ll x = 1;
            for(int i = 0; i < v[0];i++) x*=2;
            x--;
            cout<<x<<'\n';
        }else{
            pair<ll,ll> pa ={-2,-1};
            for(int i = 1; i < n; i++){
                if(v[i-1] - v[i] > pa.first){
                    pa = {v[i-1]-v[i],i};
                }
            }
            vector<ll> ans(n);
            ll x = 1;
            for(int i = 1; i <=pa.first+1;i++) x*=2;

            for(int j = pa.first+2; j <=pa.first+v[pa.second];j++) x^=(1LL<<j);
            ans[pa.second] = x;
            for(int i = pa.second-1; i>=0;i--) ans[i] = ans[i+1]-1;
            for(int i = pa.second+1;i <n;i++) ans[i] = ans[i-1]+1;
            bool ok = true;
            for(int i = 0 ; i < n; i++){
                if(ans[i] <0 || __builtin_popcountll(ans[i])!= v[i]) ok = false;
            }
            if(ok){
            cout<<ans[0]<<'\n';
            }else cout<<-1<<'\n';
        }
    }
}