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:
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;
public class GFG {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t!=0){
		    t--;
		    int n = sc.nextInt();
		    long a[] = new long[n+2];
		    for(int i=0;i<n+2;i++){
		        a[i]=sc.nextLong();
		    }
		    for(int i=0;i<n+1;i++){
		        if(a[i]>a[i+1]){
		            long temp = a[i];
		            a[i] = a[i+1];
		            a[i+1] = temp;
		        }
		    }
		    long s=0;
		    for(int i=0;i<n;i++){
		        if(a[i]>a[i+1]){
		           long temp = a[i];
		            a[i] = a[i+1];
		            a[i+1] = temp;
		        }
		        s+=a[i];
		    }
		    
		    
		    if(s==a[n])
		    {
		        for(int i=0;i<n;i++){
		            System.out.print(a[i]+" ");
		        }
		        System.out.println("");
		    }
		    else{
		        s+=a[n];
		       
		        long x = s-a[n+1];
		        int f=0,ind=-1;
		        for(int i=0;i<n+1;i++){
		            if(a[i]==x){
		                f=1; ind =i;
		            }
		        }
		        if(f==0){
		            System.out.println("-1");
		        }else{
		            for(int i=0;i<n+1;i++){
		                if(i!=ind)
		            System.out.print(a[i]+" ");
		            }
		            System.out.println("");
		        }
		    }
		}
	}
}