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;
long long b[200005];
int main()
{
	int t;
	cin>>t;
	while(t--)
	{
		map<long long ,int >q;
		int n;
		scanf("%d",&n);
		for(int i=1;i<=n+2;i++)
		{
			scanf("%lld",&b[i]);
			q[b[i]]++;
		}
		sort(b+1,b+1+2+n);
		long long sum=0;
		for(int i=1;i<=n+1;i++)
		{
			sum+=b[i];
		}
		long long c=sum-b[n+2];
		q[b[n+2]]--;
		if(q[c])
		{
			q[c]--;
			for(auto x:q)
			{
				for(int i=0;i<x.second;i++)
				{
					cout<<x.first<<" ";
				}
			}
			cout<<endl;
		} 
		else 
		{
			long long s=0;
			for(int i=1;i<=n;i++)
			{
				s+=b[i];
			}
			if(b[n+1]==s)
			{
				for(int i=1;i<=n;i++)
				{
					cout<<b[i]<<" ";
				}
				cout<<endl;
			}
			else cout<<-1<<endl;
		}
	}
	return 0;
}