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 codeforce.div3.r713;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

/**
 * @author pribic (Priyank Doshi)
 * @since 10/04/21
 */
public class D {

  public static void main(String[] args) {
    try (Scanner sc = new Scanner(System.in)) {
      int T = sc.nextInt();
      for (int tt = 1; tt <= T; tt++) {
        int n = sc.nextInt();
        // System.out.println("str.toString() = " + Arrays.toString(str));
        List<Long> arr = new ArrayList<>(n + 2);
        long sum = 0;
        for (int i = 0; i < n + 2; i++) {
          long val = sc.nextLong();
          arr.add(val);
          sum += val;
        }
        Collections.sort(arr);
        //suppose guess is >= sum
        if (sum - arr.get(n + 1) - arr.get(n) == arr.get(n) || sum - arr.get(n + 1) - arr.get(n) == arr.get(n + 1)) {
          for (int i = 0; i < n; i++) {
            long num = arr.get(i);
            System.out.print(num + " ");
          }
          System.out.println();
        } else { // guess is < sum
          //so each number upto n can be guess
          boolean found = false;
          for (int i = 0; i < n; i++) {
            long tempSum = sum - arr.get(n + 1) - arr.get(i);
            if (tempSum == arr.get(n + 1)) {
              long t = arr.get(i);
              arr.set(i, arr.get(n));
              arr.set(n, arr.get(n + 1));
              arr.set(n + 1, t);
              found = true;
              break;
            }
          }

          if (!found) {
            System.out.println(-1);
          } else {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < n; i++) {
              sb.append(arr.get(i)).append(" ");
            }
            System.out.println(sb);
          }
        }
      }
    }
  }
}