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.*;
 
public class corruptedArray2 {
	public static void main(String[] args) throws IOException {
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(f.readLine());
		StringBuilder fout = new StringBuilder();
		while(t -- > 0) {
			int n = Integer.parseInt(f.readLine()) + 2;
			long[] nums = new long[n];
			long sum = 0;
			StringTokenizer st = new StringTokenizer(f.readLine());
			HashSet<Long> numSet = new HashSet<Long>();
			HashMap<Long, Long> dict = new HashMap<Long, Long>();
			for(int i = 0; i < n; i++) {
				nums[i] = Integer.parseInt(st.nextToken());
				numSet.add(nums[i]);
				dict.put(nums[i], dict.getOrDefault(nums[i], (long) 0) + 1);
				sum += nums[i];
			}
			long ansSum = -1;
			long ansX = -1;
			for(int i = 0; i < n; i++) {
				if(numSet.contains(sum - 2 * nums[i])) {
					if(sum - 2 * nums[i] == nums[i]) {
						if(dict.get(nums[i]) >= 2) {
							ansSum = nums[i];
							ansX = sum - 2 * nums[i];
						}
					}
					else {
						ansSum = nums[i];
						ansX = sum - 2 * nums[i];
					}
				}
			}
			if(ansSum == -1 && ansX == -1) {
				fout.append("-1\n");
			}
			else {
				for(int i = 0; i < n; i++) {
					if(nums[i] == ansSum) {
						ansSum = -1;
					}
					else if(nums[i] == ansX) {
						ansX = -1;
					}
					else {
						fout.append(nums[i]).append(" ");
					}
				}
				fout.append("\n");
			}
		}
		System.out.println(fout);
	}
}