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.Scanner;
import java.util.Arrays;
import java.util.Vector;
import java.util.Collections; 


public class Problem_Solving1 {
    
  public static int binarySearch(Vector<Long> arr, long x)
{
 int l = 0 , r = arr.size()-1;
 while(l <= r )
 {
  int mid = l + (r - l )/2;
  if (arr.get(mid) ==  x)
      return 1 ;
  else if (arr.get(mid) > x )
      r = mid - 1;
  else 
      l = mid + 1;
 }
 return -1;

}
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        while (t --> 0) {
          long sm1 = 0 , sm2 = 0 ;  
          int n = input.nextInt();
          Vector<Long> arr = new Vector<Long>(n + 2);
          
            for (int i = 0; i <= n + 1; i++) {
                long x = input.nextLong();
                arr.add(x);
                sm1 += x ;
            }
            
            Collections.sort(arr);
            
            long list[] = new long[n];
            for (int i = 0; i < list.length; i++) {
                list[i] = arr.get(i);
                sm2 += list[i];
            }
            
            long mx = arr.get(n + 1);
            long mx2 = arr.get(n);
            if (sm2 == mx || sm2 ==mx2 )
            {
                for (int i = 0; i < list.length; i++) {
                    System.out.print(list[i] + " ");
                }
                System.out.println();
            
            }
            else
            {
                arr.remove(mx);
                long x = sm2 + mx2;
                long y = x - mx ;
                int r = binarySearch(arr, y);
                if (r == -1)
                    System.out.println("-1");
                else
                {
                arr.remove(y);
                 for (int i = 0; i < arr.size(); i++) {
                    System.out.print(arr.get(i) + " ");
                }
                System.out.println();
                    
                }
            
            }
           
            
          
        
          
          
        }

    }
}