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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

/**
 * Accomplished using the EduTools plugin by JetBrains https://plugins.jetbrains.com/plugin/10081-edutools
 */

public class Main {
   public static void main(String[] args) throws IOException {
      // Write your solution here
      BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
      StringBuilder output = new StringBuilder();
      int t = Integer.parseInt(reader.readLine());
      Random random = new Random();
      while (t-- > 0) {
         int n = Integer.parseInt(reader.readLine());
         int[] arr = new int[n + 2];
         StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
         for (int i = 0; i < n + 2; ++i) {
            arr[i] = Integer.parseInt(tokenizer.nextToken());
         }

         for (int i = 0; i < n + 2; ++i) {
            int j = random.nextInt(n + 2);
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
         }
         Arrays.sort(arr);

         long sum = 0;
         for (int i = 0; i < n; ++i) {
            sum += arr[i];
         }
         if (sum == arr[n]) {
            for (int i = 0; i < n; ++i) {
               output.append(arr[i]);
               output.append(' ');
            }
            output.append('\n');
            continue;
         }

         sum = 0;
         for (int i = 0; i < n + 1; ++i) {
            sum += arr[i];
         }

         long diff = (sum - arr[n + 1]);
         boolean contains = false;
         for (int i = 0; i < n + 1; ++i) {
            if (arr[i] == diff) {
               contains = true;
               break;
            }
         }
         if (contains) {
            boolean removed = false;
            for (int i = 0; i < n + 1; ++i) {
               if (arr[i] == diff && !removed) {
                  removed = true;
               } else {
                  output.append(arr[i]);
                  output.append(' ');
               }
            }
            output.append('\n');
         } else {
            output.append("-1\n");
         }
      }

      System.out.print(output);
      reader.close();
   }
}