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 <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;

const int N=200005;
//
int T,n,b[N];
long long sum;
bool flag;

int main(){
	scanf("%d",&T);
	while (T--){
		sum=0;
		flag=false;
		scanf("%d",&n);
		for (int i=1;i<=n+2;++i){
			scanf("%d",&b[i]);
			sum+=b[i];
		}
		sort(b+1,b+n+3);
		for (int i=1;i<=n+1;++i){
			if (sum-b[n+2]-b[i]==b[n+2]){
				for (int j=1;j<=n+1;++j){
					if (j==i||j==n+2) continue;
					printf("%d ",b[j]);
				}
				flag=true;
				break;
			}
		}
		if (flag==false&&sum-b[n+2]-b[n+1]==b[n+1]){
			for (int i=1;i<=n;++i){
				printf("%d ",b[i]);
			}
			flag=true;
		}
		if (flag==false) printf("-1");
		puts("");
	}
	return 0;
}