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;

const ll inf=1e17;


int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    #ifndef ONLINE_JUDGE
		freopen("input.txt","r",stdin);
		freopen("output.txt","w",stdout);
    #endif

	int t;
	cin>>t;

	while(t--){
		int n;
		cin>>n;

		vector<int> b(n+2);
		vector<int> ans;
		ll sum = 0;

		for(int i=0;i<n+2;i++){
			cin>>b[i];
			sum+=b[i];
		}

		multiset<int> have(b.begin(),b.end());
		

		for(auto x:b){
			have.erase(have.find(x));
			sum-=x;

			if(sum%2==0 && sum<=2e9 && have.find(sum/2)!=have.end()){
				have.erase(have.find(sum/2));
				for(auto y:have){
					ans.push_back(y);
				}
				break;
			}

			sum+=x;
			have.insert(x);
		}

		if((int)ans.size()!=n){
			cout<<"-1";
		}
		else{
			for(auto x:ans){
				cout<<x<<" ";
			}
		}
		cout<<endl;
	}
	
	
}