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.Arrays;
import java.util.Scanner;
 
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt();
			Long b[]=new Long[n+2];
			for(int i=0;i<n+2;i++) {
				b[i]=sc.nextLong();
			}
			Arrays.sort(b);
			long sum=0;
			for(int i=0;i<n+1;i++) {
				sum+=b[i];
			}
			int id=-1;
			for(int i=0;i<n;i++) {
				if((sum-b[i])==b[n+1]) {
					id=i;
					break;
				}
			}
			if(id==-1) {
				sum-=b[n];
				if(sum==b[n+1]) id=n;
				else if(sum==b[n]) id=n;
			}
			if(id==-1) {
				System.out.println(-1);
			}
			else {
				for(int i = 0;i < n + 1;i ++)
				{
					if(i != id) {
						System.out.print(b[i] + " ");
					}
				}
				System.out.println();
			}
		}
	}
}