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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	private static Scanner scanner;

	static {
		scanner = new Scanner(System.in);
	}

	public static void main(String[] args) {

		int T = scanner.nextInt();

		for (int t = 0; t < T; t++) {

			int n = scanner.nextInt();

			List<Long> b = new ArrayList<Long>();

			for (int i = 0; i < n + 2; i++) {
				b.add(scanner.nextLong());
			}

			Collections.sort(b);

			long sum = 0L;
			for (int i = 0; i < n + 1; i++) {
				sum += b.get(i);
			}

			int ind = -1;
			for (int i = 0; i < n + 1; i++) {
				if (sum - b.get(i) == b.get(n + 1)) {
					ind = i;
					break;
				}
			}

			if (ind == -1) {
				sum -= b.get(n);
				if (sum == b.get(n)) {
					for (int i = 0; i < n; i++) {
						System.out.print(b.get(i));
						if (i < n - 1)
							System.out.print(" ");
					}
				} else {
					System.out.print(-1);
				}
			} else {
				for (int i = 0; i < n + 1; i++) {
					if (i != ind) {
						System.out.print(b.get(i));
						if (i < n)
							System.out.print(" ");
					}
				}
			}
			System.out.println();
		}

		scanner.close();
	}
}