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.*;

public class javatest {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t=sc.nextInt();
		for (int a=0;a<t;a++) {
			int n=sc.nextInt();
			n+=2;
			long[] arr=new long[n];
			long sum=0;
			for (int j=0;j<n;j++) {
				arr[j]=sc.nextLong();
				sum+=arr[j];
			}
			find(arr,n,sum);
		}
	}
	
	public static void find(long[] arr,int n,long sum) {
		HashMap<Long,Integer> map=new HashMap<>();
		for (int i=0;i<n;i++) {
			map.put(arr[i], i);
		}
		int pos=-1,pos2=-1;
		for (int i=0;i<n;i++) {
			long num=arr[i];
			if ((sum-num)%2==0&&map.containsKey((sum-num)/2)){
				pos=i;
				pos2=map.get((sum-num)/2);
				if (pos!=pos2) break;
			}
		}
		if (pos==pos2||pos==-1||pos2==-1) {
			System.out.print(-1);
			System.out.println();return;
		}
		for (int i=0;i<n;i++) {
			if (i!=pos&&i!=pos2)
				System.out.print(arr[i]+" ");
		}
		System.out.println();
	}
	
}