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.util.ArrayList;
// import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;


public class CorruptedArray {
    public static void main(String[] args) throws IOException{
        BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
        int t1 = Integer.parseInt(r.readLine());
        while(t1 -- > 0){
            int n = Integer.parseInt(r.readLine()) + 2;
            int[] arr = new int[n];
            ArrayList<Integer>sort = new ArrayList<>();
            StringTokenizer t = new StringTokenizer(r.readLine());
            long sum = 0;
            for(int i = 0; i < n; i ++){
                sort.add(Integer.parseInt(t.nextToken()));
                arr[i] = sort.get(i);
                sum += arr[i];
            }

            Collections.sort(sort);
            boolean f = false;
            
            for(int i = 0; i < n && !f; i ++){
                long want = sum - arr[i];
                int max = (arr[i] == sort.get(n - 1)) ? sort.get(n - 2) : sort.get(n - 1);
                // System.out.println(want + " " + max);
                if(want == ((long)max) * 2L){
                    StringBuilder b = new StringBuilder();
                    boolean skip = false;
                    for(int j = 0; j < n; j ++){
                        if(i == j)
                            continue;
                        if(!skip && max == arr[j]){
                            skip = true;
                            continue;
                        }
                        b.append(arr[j]);
                        b.append(" ");
                    }
                    System.out.println(b);
                    f = true;
                    break;
                    
                }

                
            }
            if(!f)
                System.out.println(-1);
        }
    }
        
}