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.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class D_Corrupted_Array
{
    public static void main (String[] args) throws java.lang.Exception
    {
          FastReader fs = new FastReader();
          PrintWriter out =new PrintWriter(System.out);
          int t= fs.nextInt();
          for(int i=0;i<t;i++)
          {
              
              //String ann="";
              int n=fs.nextInt();
            //  long a[]=new long[n];
              long b[]=new long[n+2];
              long sum=0;
              long sum2=0;
              long sum3=0;
              for(int j=0;j<n+2;j++){
                b[j]=fs.nextLong();
                sum=sum+b[j];
              }
              sum3=sum;
              ruffleSort(b);
              sum=sum-b[n+1];
              sum3=sum3-b[n+1]-b[n];
              if(sum3==b[n]||sum3==b[n+1]){
                for(int j=0;j<n;j++)
                out.print(b[j]+" ");
                out.println();
                continue;
              }
              sum2=sum;
              int index=-1;
              for(int j=0;j<n+1;j++){
                  sum2=sum2-b[j];
                  if(sum2==b[n+1]){
                    index=j;
                    break;
                  }
                  sum2=sum;
              }
              if(index==-1){
                  out.println(-1);
              }
              else{
                  for(int j=0;j<n+1;j++){
                      if(j!=index){
                          out.print(b[j]+" ");
                      }
                  }
                  out.println();
              }
             
          }
          out.flush();
 }
        
 static void ruffleSort(long arr[])
 {
     int n = arr.length;
     for(int i=0; i<n; i++)
     {
         Random r=new Random();
         int j = r.nextInt(n);
         long temp = arr[j];
         arr[j] = arr[i];
         arr[i] = temp;
     }
     Arrays.sort(arr);
 }
        static class FastReader 
        {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            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;
        }
    }
}