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 JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.HashMap;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.io.*;
 
public class CorruptedArr {
	
	private static class MyScanner {
	    BufferedReader br;
	    StringTokenizer st;

	    public MyScanner() {
	       br = new BufferedReader(new InputStreamReader(System.in));
	    }

	    String next() {
	        while (st == null || !st.hasMoreElements()) {
	            try {
	                st = new StringTokenizer(br.readLine());
	            } catch (IOException e) {
	                e.printStackTrace();
	            }
	        }
	        return st.nextToken();
	    }

	    int nextInt() {
	        return Integer.parseInt(next());
	    }

	    long nextLong() {
	        return Long.parseLong(next());
	    }

	    double nextDouble() {
	        return Double.parseDouble(next());
	    }

	    String nextLine(){
	        String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	    }

	 }
	

	
	public static void solution(int[] list, int n)
			
	{
		ArrayList<Integer> arr = new ArrayList<>();
		
		for(int i = 0; i<n+2; i++)
			arr.add(list[i]);
		
		Collections.sort(arr);
		
		long s = arr.get(n);
		long sum = 0;
		
		for(int i = 0; i<n; i++)
		{
			sum+=arr.get(i);
		}
		
		if(sum==s)
		{			
		   for(int i = 0; i<n; i++)
		     out.print(arr.get(i)+" ");
		
		return; }
		
		s = arr.get(n+1);
		sum = 0;
		
		for(int i = 0; i<n+1; i++)
			sum+=arr.get(i);
		
		if(sum<=s)
		{
			out.print(-1);
			return;
		}
		
		long req = sum-s;
		int in = -1;
		int i = 0;
		
		for(i = 0; i<n+1; i++)
		{
			if(arr.get(i)==req)
			{
				in = i; break;
			}
		}
		
		if(i==n+1)
		{
			out.print(-1);
			return;
		}
		
		for(i = 0; i<n+1; i++)
		{
			if(i!=in)
				out.print(arr.get(i)+" ");
			else
				continue;
		}
		
	}
        
private static PrintWriter out = new PrintWriter(System.out);

public static void main (String[] args)
{
	MyScanner s =  new MyScanner();
     
    int t = s.nextInt();
    
    for(int j = 0; j<t ; j++)
    {
    	int n = s.nextInt();
    	int[] arr = new int[n+2];
    	for(int i =0; i<n+2; i++)
    		arr[i] = s.nextInt();
    	
    	solution(arr,n);
    	
    	out.println();
    }
    
    out.flush();
    out.close();
    
}
}