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.io.*;
import java.lang.*;
import java.math.BigInteger;
import java.util.*;
public class Main{
	static Scanner scanner=new Scanner(System.in);
	static BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
	public static void main(String[] args) throws NumberFormatException, IOException {
		int q=scanner.nextInt();
		StringBuilder sbb=new StringBuilder();
		l:while(q-->0) {
			int n=scanner.nextInt();
			Long a[]=new Long [n+2];
			Long b[]=new Long[n+2];
			for(int i=0;i<n+2;i++) {
				a[i]=scanner.nextLong();
			}
			Arrays.sort(a);
			for(int i=0;i<n+2;i++)b[i]=a[i];
			for(int i=1;i<n+2;i++) {
				a[i]+=a[i-1];
			}
			StringBuilder sb=new StringBuilder();
			if(a[n]==2*a[n-1]) {
				for(int i=0;i<n;i++) {
					sb.append(b[i]+" ");
				}
				if(q!=0)sbb.append(sb+"\n");
				else sbb.append(sb);
				continue l;
			}else {
				for(int i=0;i<=n;i++) {
					if(a[n]-b[i]==b[n+1]) {
						for(int j=0;j<=n;j++) {
							if(i!=j)sb.append(b[j]+" ");
						}
						if(q!=0)sbb.append(sb+"\n");
						else sbb.append(sb);
						continue l;
					}
				}
			}
			if(q!=0)sbb.append(-1+"\n");
			else sbb.append(-1);
		}
		System.out.println(sbb);
	}
}