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 IOS ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
int lowbit(int x)
{
	return x&(-x);
}
int b[210000],a[210000],sm[210000];
signed main()
{
	int t;
	cin>>t;
	while(t--)
	{
		int n,i,j;
		int flag=0,sum=0;
		scanf("%lld",&n);
		for(i=1; i<=n+2; i++)
		{
			scanf("%lld",&b[i]);
			sum+=b[i];
		}
		sort(b+1,b+n+1+2);
		sum=sum-b[n+2];
		int cnt=0;
		int dai;
		for(i=1; i<=1+n; i++)
		{
			sm[++cnt]=sum-b[i];
		}
		for(i=1; i<=cnt-1; i++)
		{
			if(sm[i]==b[n+2])
			{
				dai=i;
				flag=1;
				break;
			}
		}
		if(sm[cnt]==b[n+1]||sm[cnt]==b[n+2])
		{
			dai=cnt;
			flag=1;
		}
		if(flag)
		{
			if(dai!=1)cout<<b[1];
			for(i=2; i<=n+1; i++)
			{
				if(dai==1&&i==2)cout<<b[i];
				else if(i!=dai)cout<<" "<<b[i];
			}
			cout<<endl;
		}
		else cout<<"-1"<<endl;
	}
}