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.*;

public class Solution {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt() + 2;
            long sum = 0;
            int arr[] = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = sc.nextInt();
                sum += arr[i];
            }
            int maxInd = 0;
            for (int i = 1; i < n; i++) {
                if (arr[maxInd] < arr[i]) {
                    maxInd = i;
                }
            }
            int iInd = -1;
            int jInd = -1;
            for (int i = 0; i < n; i++) {
                if (i == maxInd)
                    continue;
                sum -= arr[i];
                if (sum - arr[maxInd] == arr[maxInd]) {
                    iInd = i;
                    jInd = maxInd;
                    break;
                }
                sum += arr[i];
            }
            if (iInd == -1) {
                int nextMaxInd = maxInd == 0 ? 1 : 0;
                for (int i = 0; i < n; i++) {
                    if (i == maxInd)
                        continue;
                    if (arr[i] > arr[nextMaxInd]) {
                        nextMaxInd = i;
                    }
                }
                sum -= arr[maxInd];
                if (sum - arr[nextMaxInd] == arr[nextMaxInd]) {
                    iInd = maxInd;
                    jInd = nextMaxInd;
                }
            }
            if (iInd == -1) {
                System.out.println(-1);
                continue;
            }
            for (int i = 0; i < n; i++) {
                if (i == iInd || i == jInd)
                    continue;
                System.out.print(arr[i] + " ");
            }
            System.out.println();
        }
    }
}