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:
// Don't place your source in a package
import java.lang.reflect.Array;
import java.text.DecimalFormat;
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
import java.util.stream.Stream;


// Please name your class Main
public class Main {
    static FastScanner fs=new FastScanner();
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next() {
            while (!st.hasMoreElements())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        int Int() {
            return Integer.parseInt(next());
        }

        long Long() {
            return Long.parseLong(next());
        }

        String Str(){
            return next();
        }
    }


    public static void main (String[] args) throws java.lang.Exception {
        PrintWriter out = new PrintWriter(System.out);


        int T=Int();
        for(int t=0;t<T;t++){
            int n=Int();
            long A[]=new long[n+2];
            for(int i=0;i<A.length;i++){
                A[i]=Long();
            }

            Solution sol=new Solution(out);
            sol.solution(A);
        }
        out.flush();

    }


    public static int Int(){
        return fs.Int();
    }
    public static long Long(){
        return fs.Long();
    }
    public static String Str(){
        return fs.Str();
    }

}






class Solution{
    PrintWriter out;
    public Solution(PrintWriter out){
        this.out=out;
    }





    public void solution(long A[]){
        sort(A);
        long sum=0;
        long sum1=0;

        for(int i=0;i<A.length-1;i++){
            sum+=A[i];
        }
        for(int i=0;i<A.length-2;i++){
            sum1+=A[i];
        }

        if(sum1==A[A.length-2]){
            for(int j=0;j<A.length-2;j++){
                out.print(A[j]+" ");
            }
            out.println();
            return;
        }


        for(int i=0;i<A.length-1;i++){
            if(sum-A[i]==A[A.length-1]){
                for(int j=0;j<A.length-1;j++){
                    if(j==i)continue;
                    out.print(A[j]+" ");
                }
                out.println();
                return;
            }
        }




        out.println(-1);


    }

    public void sort(long A[]){
        PriorityQueue<Long>pq=new PriorityQueue<>();
        for(long i:A)pq.add(i);
        for(int i=0;i<A.length;i++)A[i]=pq.poll();
    }



}

//1 2 2 6 9


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                      free bug dog
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