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

public class Solution {

	int n;
	Integer[] nums;

	public Solution(Scanner in){
		this.n = in.nextInt() + 2;
		this.nums = new Integer[this.n];
		for(int i=0; i<this.n; i++){
			this.nums[i] = in.nextInt();
		}
	}

	private String printAllBut(int i1, int i2){
		StringBuilder sb = new StringBuilder();
		boolean first = true;
		for(int i=0; i<this.n; i++){
			if(i == i1 || i == i2){
				continue;
			}
			if(first){
				first = false;
			} else {
				sb.append(" ");
			}
			sb.append(this.nums[i]);
		}
		return sb.toString();
	}
	
	public String solve(){
		long sum = 0;
		int max = 0;
		int maxIndex = -1;
		for(int i=0; i<this.n; i++){
			int curr = this.nums[i];
			if(curr > max){
				max = curr;
				maxIndex = i;
			}
			sum += curr;
		}
		long rem = sum - max - max;
		int extraIndex = -1;
		for(int i=0; i<this.n; i++){
			if(i == maxIndex){
				continue;
			}
			int curr = this.nums[i];
			if(curr == rem){
				extraIndex = i;
				break;
			}
		}

		if(extraIndex >= 0){
			return this.printAllBut(maxIndex, extraIndex);
		}

		extraIndex = maxIndex;
		sum = 0;
		max = 0;
		maxIndex = -1;
		for(int i=0; i<this.n; i++){
			if(i == extraIndex){
				continue;
			}
			int curr = this.nums[i];
			if(curr > max){
				max = curr;
				maxIndex = i;
			}
			sum += curr;
		}

		if(max == sum - max){
			return this.printAllBut(maxIndex, extraIndex);
		}

		return "-1";
	}

	public static void main(String[] args){	
		try(
			Scanner in = new Scanner(System.in);
			){
			int T = in.nextInt();
			for(int i=1; i<=T; i++){
				Solution solution = new Solution(in);
				System.out.println(solution.solve());
			}
		}
		System.exit(0);
	}

}