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.*;

public class D {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = in.nextInt();
        for (int t1 = 0; t1 < t; t1++) {
            int n = in.nextInt() + 2;
            Long[] arr = new Long[n];
            for (int i = 0; i < n; i++) arr[i] = in.nextLong();
            pw.println(solve(arr, n));
        }

        pw.close();
    }

    static StringBuilder solve(Long[] arr, int n) {
        StringBuilder sb = new StringBuilder();
        Arrays.sort(arr);
        long sum = 0;
        for (int i = 0; i < n; i++) sum += arr[i];
        {
            long possible = arr[n - 1];
            long temp = sum - possible;
            int cut = -1;
            for (int i = 0; i < (n - 1); i++) {
             //   debug(sum - arr[i], sum, arr[i], possible);
                if ((temp - arr[i]) == possible) {
                    cut = i;
                    break;
                }
            }
         //   debug(cut);
            if (cut != -1) {
                for (int i = 0; i < n; i++) {
                    if (i == cut || i == (n - 1)) continue;
                    sb.append(arr[i] + " ");
                }
                return sb;
            }
        }
        sum -= arr[n - 1];
        sum -= arr[n - 2];
        if (sum == (arr[n - 2])) {
         //   debug(sum);
            for (int i = 0; i < (n - 2); i++) {
                sb.append(arr[i] + " ");
            }
            return sb;
        }
        return sb.append(-1);
    }


    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}