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;

int main(){
	int t;
	cin>>t;
	//sum has to be one of the max two elements
	while(t--){
		int n;
		cin>>n;
		int b[n+2];
		for(int i=0;i<n+2;i++){
			cin>>b[i];
		}
		long long int sum=0;
		int max,second_max;
		max=second_max=-1;
		int max_index,second_max_index;

		for(int i=0;i<n+2;i++){
			sum+=b[i];
			if(b[i]>second_max){
				if(b[i]>max){
					second_max=max;
					second_max_index=max_index;
					max=b[i];
					max_index=i;
				}
				else {
					second_max=b[i];
					second_max_index=i;
				}
			}
		}
		long long int sum1,sum2;
		sum1=sum-max;
		sum2=sum-second_max;
		int x_index=-1;
		int final_max_index;
		for(int i=0;i<n+2;i++){
			if(i!=max_index){
				if(sum1-b[i]==max){
					x_index=i;
					final_max_index=max_index;
					break;
				}
			}
			if(i!=second_max_index){
				if(sum2-b[i]==second_max){
					x_index=i;
					final_max_index=second_max_index;
					break;
				}
			}
		}
		if(x_index==-1){
			cout<<-1<<'\n';
		}
		else {
			vector<int> a;
			for(int i=0;i<n+2;i++){
				if(i!=final_max_index and i!=x_index){
					a.push_back(b[i]);
				}
			}
			for(int i=0;i<n;i++){
				cout<<a[i]<<" ";
			}
			cout<<'\n';
		}
	}
	return 0;
}