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.lang.*;
import java.io.*;
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[] arr = new long[n+2];
				int max = 0;
				int max1 = 0;
				
				long sumTotal = 0;
				for(int i=0;i<n+2;i++) {
					arr[i] = sc.nextLong();
					sumTotal += arr[i];
					if(arr[i]>=arr[max]) {
						max = i;
					}
				}
				if(max==0)max1++;
				for(int i=0;i<n+2;i++){
				    if(i==max)continue;
				    else if(arr[i]>=arr[max1])max1 = i;
				}
			
				long sum = sumTotal - arr[max];
				boolean poss = false;
				int ind = 0;
				for(int i=0;i<n+2;i++) {
					if(i!=max && sum - arr[i] == arr[max]) {
						poss = true;
						ind = i;
						break;
					}
				}
				if(!poss){
				    if(sum - arr[max1] == arr[max1]){
				        poss = true;
				        ind = max1;
				    }
				}
				
				
				if(poss) {
				for(int i =0;i<n+2;i++) {
					if(i!=max && i!=ind)System.out.print(arr[i] + " ");
				}
				System.out.println();
				}
				else System.out.println("-1");
				t--;
				
			}
			
    }
}