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.*;
public class Main  {
    public static void main(String args[]) {
      FastScanner fs=new FastScanner();    
      PrintWriter out=new PrintWriter(System.out);
      
      
      int t=fs.nextInt();
     l1: while(t-->0)
      {
      int n=fs.nextInt();
      
      
      long arr[]=fs.readArray(n+2);
      
      int i;
      
      sort(arr);
      
      long sum=0;
      
      for(i=0;i<n;i++)
      sum+=arr[i];
      
      boolean flag=false;
      if(sum==arr[n+1] || sum==arr[n])
      {
          for(i=0;i<n;i++)
          out.print(arr[i]+" ");
          out.println();
          continue l1;
      }
      int last=n;
      int del=0;
      for(i=0;i<n;i++)
      {
          sum+=arr[last];
          sum-=arr[i];
          if(sum==arr[n+1])
          {
              flag=true;
              del=i;
              break;
          }
          last=i;
      }
      if(flag)
      {
      for(i=0;i<n+1;i++)
      {
          if(i!=del)
          out.print(arr[i]+" ");
      }
      out.println();
      }
      else
      out.println(-1);
     
      }
      
        out.flush();
        out.close();
    }
    static void sort(long a[]){
	    ArrayList<Long> al=new ArrayList<>();
	    for(long x:a)al.add(x);
	    Collections.sort(al);
	    for(int i=0;i<a.length;i++) a[i]=al.get(i);
	}
}
        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();
		}
		String nextLine() {
		    String str="";
		    try {
		        str=br.readLine();
		    }
		    catch (IOException e) {
		        e.printStackTrace(); 
		    }
		    return str;
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		long[] readArray(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}