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.*;


public class Main
{   
    static void sort(long a[])
    {
        Random ran = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = ran.nextInt(a.length);
            long temp = a[r];
            a[r] = a[i];
            a[i] = temp;
        }
        
        Arrays.sort(a);
    }
    public static int check(long sum,int index,long a[])
    {
        sum-=a[index];
        for (int i = 0; i < a.length; i++) {
            if(i==index)
                continue;
            else if(sum-a[i]==a[index])
            {
                return i;
            }
        }
        return -1;
    }
    public static void main(String args[])
    {
        FastScanner input = new FastScanner();
        int tc = input.nextInt();
        work:   while (tc-- > 0) {
         int n = input.nextInt();
       long a[] = new long[n+2];
       long sum = 0;
        for (int i = 0; i < n+2; i++) {
            a[i] = input.nextLong();
            sum+=a[i];
            
        }
        sort(a);
        int got = check(sum, n+1, a);
        if(got>=0)
        {
            for (int i = 0; i <n+2; i++) {
                if(i==got||i==n+1)
                {
                    continue;
                }
                else
                {
                    System.out.print(a[i]+" ");
                }
            }
            System.out.println("");
            continue work;
        }
        if(a[n]!=a[n+1])
        {
            got = check(sum, n, a);
            if(got>=0)
        {
            for (int i = 0; i <n+2; i++) {
                if(i==got||i==n)
                {
                    continue;
                }
                else
                {
                    System.out.print(a[i]+" ");
                }
            }
            System.out.println("");
            continue work;
        }
            
        }
        System.out.println("-1");   
        }
        
    }

    static class FastScanner
    {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next()
        {
            while (!st.hasMoreTokens()) {
                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() throws IOException
        {
            return br.readLine();
        }
    }

}