Problem: You are given a number n and an array b_1, b_2, …, b_{n+2}, obtained according to the following algorithm: 

  * some array a_1, a_2, …, a_n was guessed; 
  * array a was written to array b, i.e. b_i = a_i (1 ≤ i ≤ n); 
  * The (n+1)-th element of the array b is the sum of the numbers in the array a, i.e. b_{n+1} = a_1+a_2+…+a_n; 
  * The (n+2)-th element of the array b was written some number x (1 ≤ x ≤ 10^9), i.e. b_{n+2} = x; The 
  * array b was shuffled. 



For example, the array b=[2, 3, 7, 12 ,2] it could be obtained in the following ways: 

  * a=[2, 2, 3] and x=12; 
  * a=[3, 2, 7] and x=2. 



For the given array b, find any array a that could have been guessed initially.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second row of each test case contains n+2 integers b_1, b_2, …, b_{n+2} (1 ≤ b_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output: 

  * "-1", if the array b could not be obtained from any array a; 
  * n integers a_1, a_2, …, a_n, otherwise. 



If there are several arrays of a, you can output any.

Example

Input


4
3
2 3 7 12 2
4
9 1 7 1 6 5
5
18 2 2 3 2 9 2
3
2 6 9 2 1


Output


2 3 7 
-1
2 2 2 3 9 
1 2 6 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
void solve(){
	int n;
	cin >> n;
	n += 2;
	ll sum = 0;
	ll del = -1;
	
	vector<ll>ve(n);
	set<ll>se;
	
	for(int i=0; i<n; i++) cin >> ve[i];
	sort(ve.begin(), ve.end());
	
	bool ok = 0;
	for(int i = 0; i < n; i++){
		sum += ve[i];
		se.insert(ve[i]);
		if(i == n-3 && sum == ve[n-2]){
			ve.pop_back();
			ve.pop_back();
			ok = 1;
			break;
		} else if(i == n-2 && sum > ve[n-1] && se.find(sum-ve[n-1]) != se.end()){
			ve.pop_back();
			del = sum - ve[n-1];
			ok=1;
			break;
		}
	}
	if(del != -1 && ok){
		bool al = 0;
		for(auto x : ve){
			if(!al && x == del){
				al = 1;
				continue;
			}
			cout << x << " ";
		}
		cout << endl;
	} else if(ok){
		for(auto x : ve){
			cout << x << " ";
		}
		cout << endl;
	} else {
		cout << -1 << endl;
	}
}
int main(){
	int t; cin>>t;
	while(t--){
		solve();
	}
	return 0;
}