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.util.*;
 
import java.io.*;
import java.lang.*;
 
public class Problem {
 
    public static void main(String[] args) {
        MyScanner scan = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = scan.nextInt();
        while (t-- > 0) {
            int n = scan.nextInt();
            long b[] = new long[n + 2];
             long sum = 0;
            for (int i = 0; i < n + 2; i++){
                b[i] = scan.nextInt();
                sum+=b[i];
            }
 
            sort(b);
            
            sum-=(b[n]+b[n+1]);
           
 
            int drop = -1;
 
            if (sum == b[n]) {
                for (int i = 0; i < n; i++)
                    System.out.print(b[i] + " ");
                System.out.println();
            } else {
                sum+=b[n];
              for(int i=0;i<=n;i++){
                  if(sum-b[i]==b[n+1]){
                      drop=i;
                      break;
                  }
              }
              if(drop!=-1){
                  for(int i=0;i<=n;i++){
                      if(drop==i)
                      continue;
                      else System.out.print(b[i]+" ");
                  }
                  System.out.println();
              }else System.out.println(-1);
               
            }
 
        }
        out.close();
    }
       public static void sort(long[] array){
		ArrayList<Long> copy = new ArrayList<>();
		for (Long i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
 
}
 
class MyScanner {
    BufferedReader br;
    StringTokenizer st;
 
    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
 
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt() {
        return Integer.parseInt(next());
    }
 
    long nextLong() {
        return Long.parseLong(next());
    }
 
    double nextDouble() {
        return Double.parseDouble(next());
    }
 
    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
 
}