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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Shovon
 */
public class corrupted_array {
    public static void main(String[] args) throws IOException {
        InputStreamReader inputStream = new InputStreamReader(System.in);
        OutputStream outputStream = System.out;
        BufferedReader in = new BufferedReader(inputStream);
        int tc = Integer.parseInt(in.readLine());
        while (tc-- > 0) {
            int n = Integer.parseInt(in.readLine())+2;
            int[] arr = new int[n];
            ArrayList<Integer> arrayList = new ArrayList<>(n);

            String arr_string = in.readLine();
            String[] strs = arr_string.trim().split(" ");
            for (int i = 0; i < n; i++) {
                arrayList.add(Integer.parseInt(strs[i]));
            }

            Collections.sort(arrayList);

            long sum = 0;
            for (int i = 0; i < n-2; i++) {
                sum += arrayList.get(i);
            }
            if(sum == arrayList.get(n-2)){
                StringBuilder result = new StringBuilder("");
                for (int i = 0; i < n-2; i++) {
                    result.append(arrayList.get(i)+" ");
                }
                System.out.println(result);
            }
            else {
                int ops = -1;
                long  sum1 = 0;
//                    for (int i = 0; i < n+1; i++) {
//                        sum1 += arr[i];
//                    }
                sum1 = sum + arrayList.get(n-2);
                for (int i = 0; i < n-1; i++) {
                    if(arrayList.get(n-1) == sum1-arrayList.get(i)){
                        ops = i;
                        break;
                    }
                }
                if(ops == -1){
                    System.out.println("-1");
                }
                else {
                    StringBuilder result = new StringBuilder("");
                    for (int i = 0; i < n-1; i++) {
                        if(i != ops){
                            result.append(arrayList.get(i)+" ");
                        }
                    }
                    System.out.println(result);
                }
            }
        }
     }
}