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.*;

public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner scn=new Scanner(System.in);
		int t=scn.nextInt();
		while(t>0){
		    int n=scn.nextInt();
			int[] arr=new int[n+2];
			int max=Integer.MIN_VALUE;
			int maxidx=0;
			int smaxidx=0;
			int secmax=Integer.MIN_VALUE;
            for(int i=0 ; i<n+2 ; i++){
				arr[i]=scn.nextInt();
				if(arr[i]>max){
					secmax=max;
					smaxidx=maxidx;
					maxidx=i;
					max=arr[i];
				}else if(arr[i]==max){
					secmax=arr[i];
					smaxidx=i;
				}else if(secmax<arr[i]){
					secmax=arr[i];
					smaxidx=i;
				}
			}
            long sum=0;
			for(int i=0 ; i<n+2 ; i++){
				if(i!=maxidx && i!=smaxidx){
					sum+=(long)arr[i];
				}
			}
			if(sum==(long)secmax){
				for(int i=0 ; i<n+2 ; i++){
					if(i!=maxidx && i!=smaxidx){
						System.out.print(arr[i]+" ");
					}
				}
				System.out.println();
			}else{
				sum+=(long)secmax;
				int k=-1;
				for(int i=0 ; i<n+2 ; i++){
					if(i!=maxidx){
						if(sum==(long)(arr[i]+max)){
                            k=i;
							break;
						}
					}
				}
				if(k==-1){
					System.out.println(-1);
				}else{
				    for(int i=0 ; i<n+2 ; i++){
					    if(i!=maxidx && i!=k){
						     System.out.print(arr[i]+" ");
					    }
				    }
				    System.out.println();
			   }
			}
			
			t--;
		}
	}
}