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.Scanner;
import java.util.Arrays;

import java.util.ArrayList;
import java.util.Collections;
        // System.out.println();

public class d {
    public static Scanner sc = new Scanner(System.in);
    public static void main(String[] args) {
        int t = sc.nextInt();
        while(t-- > 0){
            solve();            
        }
    }

    public static void solve(){
        int n = sc.nextInt();
        ArrayList<Integer> b = new ArrayList<Integer>();
        long sum = 0;
        for(int i = 0; i < n + 2; ++i){
            int num = sc.nextInt();
            b.add(num);
            sum += num;
        }
        Collections.sort(b);

        long curSum = 0;
        for(int i = 0; i < n + 2; ++i){
            curSum = sum - b.get(i);
            if(curSum - b.get(n) == b.get(n) && i != n){
                for(int j = 0; j < n + 2; ++j){
                    if(j == i || j == n) continue;
                    System.out.print(b.get(j) + " ");
                }
                ln();
                return ;
            }
            if(curSum - b.get(n + 1) == b.get(n + 1) && i != n + 1){
                for(int j = 0; j < n + 2; ++j){
                    if(j == i || j == n + 1) continue;
                    System.out.print(b.get(j) + " ");
                }
                ln();
                return ;
            }
        }
        no();
    }

    public static void no(){
        System.out.println(-1);
    }

    public static void ln(){
        System.out.println();
    }
}