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.*;
import java.lang.*;


public class cf713 {
    
    public static void sort(int[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			int temp = arr[i];  arr[i] = arr[idx]; arr[idx] = temp;  //swap
		}
		Arrays.sort(arr);
	}
	
    
    public static void main(String[] args) throws Exception{
        InputStreamReader ip=new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(ip);
        // Scanner scn=new Scanner(System.in);
        int t = Integer.parseInt(br.readLine());
        // fill();

       while(t-->0){
        int n =Integer.parseInt(br.readLine());
        String[] strs=(br.readLine()).trim().split(" ");
        int a=Integer.parseInt(strs[0]),b=Integer.parseInt(strs[1]);//,c=Integer.parseInt(strs[2]),n=Integer.parseInt(strs[3]);
        // String str=(br.readLine()).trim();    

        int[] arr=new int[n+2];

        for(int i=0;i<n+2;i++){
            arr[i]=Integer.parseInt(strs[i]);
        }

        // Arrays.sort(arr);   mymistake TLE worst cast time complexity of  Arrays.sort(arr) is O(n^2)
        sort(arr);
        long msum1=0,msum2=0;


        for(int i=0;i<n+2;i++){
                if(i!=n+1)msum1+=(long)arr[i];
        }

        for(int i=0;i<n+2;i++){
            if(i!=n)msum2+=(long)arr[i];
         }


        long sum1=arr[n+1];
        long sum2=arr[n];

        int r1=-1,r2=-1;
        for(int i=0;i<(n+2);i++){
            if(i!=n+1 && (msum1-(long)arr[i])==sum1){
                r1=n+1;  r2=i;  break;
            }
        }

        

        for(int i=0;i<(n+2) && r1<0 && r2<0;i++){
            if(i!=n && (msum2-(long)arr[i])==sum2){
                r1=n;  r2=i;  break;
            }
         }

         if(r1>=0 && r2>=0){
            for(int i=0;i<n+2;i++){
                if(i!=r1 && i!=r2)System.out.print(arr[i]+" ");
            } 
         }else{
             System.out.print(-1);
         }
          
        System.out.println();
       }
    }
}