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

int main(){
	ios::sync_with_stdio(false),cin.tie(0);
	int t; cin >> t;
	while(t--) []{
		int n; cin >> n;
		vector<int> A(n); for (int& a:A) cin >> a;
		auto f = [](long long x) -> int {
		  return (x?64-__builtin_clzll(x)-__builtin_popcountll(x):1);
		};
		cout << [&f](this auto self,vector<int>& A) -> long long {
		  if (*min_element(A.begin(),A.end())<0) return -1;
		  int n = A.size();
		  if (n==1) return (A[0]!=1?1ll<<A[0]:0ll);
		  if (n==2){
		    if (A[0]>A[1]+1) return -1;
		    if (A[0]==0) return (A[1]?(1ll<<A[1])-1:-1ll);
		    if (A[0]==1&&A[1]==0) return 0;
		    return (1ll<<(A[1]+1))+(1ll<<(A[1]-A[0]+1))-1;
		  }
		  bool is0 = true,is1 = true;
		  for (int i(0);i < n;++i){
		    if (A[i]!=f(i)) is0 = false;
		    if (A[i]!=f(i+1)) is1 = false;
		  }
		  if (is0) return 0;
		  if (is1) return 1;
		  vector<int> B;
		  for (int i(0);i < n;i+=2) if (i+1==n||A[i+1]==A[i]-1) B.emplace_back(A[i]-1);
		  if (B.size()==(n+1)/2){
		    long long res = self(B);
		    if (res>0) return 2*res;
		    if (res==0&&n<=4) return 4;
		  }
		  B.clear();
		  B.emplace_back(A[0]);
		  for (int i(1);i < n;i+=2) if (i+1==n||A[i+1]==A[i]-1) B.emplace_back(A[i]-1);
		  if (B.size()==n/2+1){
		    long long res = self(B);
		    if (res>0) return 2*res+1;
		    if (res==0&&n==3) return 5;
		  }
		  return -1;
		}(A) << '\n';
	}();
}