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.Scanner;
import java.util.Arrays;
// import java.util.Collections;
// import java.util.ArrayList;
import java.util.HashMap;
// import java.util.ArrayList;
// import java.util.Set;
// import java.util.TreeSet;
// import java.util.stream.Collectors; 
// import java.util.stream.Stream; 
// import java.util.Stack;
// import java.util.Optional;
// import java.util.HashSet;

public class sol{
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0){ 
            int n=sc.nextInt();
           Long ar[]=new Long[n+2];
           for(int i=0;i<n+2;i++){
              ar[i]=sc.nextLong();
           }
         //   System.out.println("done");
           Arrays.sort(ar);
         //   for(int i=0;i<n+2;i++){
         //        System.out.print(ar[i]+" ");
         //   }
           long partialSum=0;
           for(int i=0;i<n;i++){
              partialSum+=ar[i];
           }
            // System.out.println("done2 partial sum="+partialSum);
         // System.out.println(ar[n]);
         // System.out.println(ar[n+1]);

           if(partialSum==ar[n]||partialSum==ar[n+1])
           {
               // System.out.println("done3  if");
              for(int i=0;i<n;i++){
                 System.out.print(ar[i]+" ");
              }
              System.out.println();

           }
           else{
                     //  System.out.println("done3 else");
              boolean flag=true;
              String ans="";
            //   int k=0;
              int tempans=0;
               partialSum+=ar[n];
               HashMap<Long,Integer> hm=new HashMap<>();

               for(int j=0;j<n+1;j++){
                  hm.put(ar[j],1);
               }
               if(hm.containsKey(partialSum-ar[n+1]))
               {
                  // int k=0;
                  int g=0;
                  for(int k=0;k<n+1;k++){
                     if(g==0&&ar[k]==(partialSum-ar[n+1]))
                     {
                        g=1;
                     }
                     else
                     System.out.print(ar[k]+" ");
                  }
                  System.out.println();
               }

            //   System.out.println(flag);
              else
              System.out.println("-1");

           }
         

               

                 }
    }
}