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>
#define int long long 
#define endl '\n'
using namespace std;


void solve()
{
	int n;
	cin >> n;
	int a[n+2];

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

	sort(a,a+n+2);
	int sum = 0;
	for(int i=0;i<n;i++)
	{
		sum += a[i];
	}
	// cout << sum << endl;
	if(sum==a[n]||sum==a[n+1])
		{

			for(int i=0;i<n;i++)
			{
				cout << a[i] << " ";
			}
			cout << endl;
			return;
		}

		sum += a[n];

	if(sum>=a[n+1])
	{
		
		
		{
			// cout << sum + a[n] << endl;
			for(int i=0;i<n+1;i++)
			{
				if(sum-a[i]==a[n+1])
				{
					for(int j=0;j<n+1;j++)
					{
						if(j!=i)
						{
							cout << a[j] << " ";
						}
					}
					cout << endl;
					return;
				}
			}
			cout << -1 << endl;
		}

		
	}
	else
	{
		cout << -1 << endl;
	}
}
int32_t main()
{
	int t;
	cin >> t;
	while(t--)
	{
		solve();
	}
}