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:
/******************************************************************************

                            Online Java Compiler.
                Code, Compile, Run and Debug java program online.
Write your code in this editor and press "Run" button to execute it.

*******************************************************************************/
import java.io.*;
import java.util.*;
public class Main
{
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
// Scanner foo = new Scanner(System.in);
		int t = Integer.parseInt(br.readLine());
// int t = foo.nextInt();
		for(int q=0;q<t;q++){
		    int n = Integer.parseInt(br.readLine());
		  //int n = foo.nextInt();
		    String s[] = br.readLine().split(" ");
		  //  int a[] = new int[n+2];
		  Integer a[] = new Integer[n+2];
		    long sum = 0;
		    for(int i=0;i<n+2;i++){
		        a[i] = Integer.parseInt(s[i]);
		    }
		    Arrays.sort(a);
		    for(int i=0;i<n+2;i++){
		        sum+=a[i];
		    }
		    sum = sum - a[n+1] - a[n];
		    if(sum==(long)a[n]){
                StringBuffer sb = new StringBuffer();
		        for(int i=0;i<n;i++){
		            sb.append(a[i] + " ");
		        }
		        System.out.println(sb);
		    }
		  else{
    		sum+=a[n];
    		int k=-1;
    		for(int i=0;i<=n;i++){
    			if(sum-a[i]==a[n+1]){
    				k=i;
    				break;
    			}
    		}
    		if(k==-1)
    		System.out.println(-1);
    		else{
    		    StringBuffer sb = new StringBuffer();
    			for(int i=0;i<=n;i++){
    				if(i!=k)
    				sb.append(a[i]+" ");
    			}
    			System.out.println(sb);
    		}
    	}
		}
	}
}