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:
/*
Written by Kabir Kanha Arora
@kabirkanha
 */

import java.util.*;
import java.io.*;

public class Main {

    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int t = scanner.nextInt();
        while (t-- > 0) {
            int n = scanner.nextInt() + 2;
            ArrayList<Long> list = new ArrayList<>();
            long sum = 0;
            for (int i = 0; i < n; ++i) {
                long input = scanner.nextLong();
                list.add(input);
                sum += input;
            }
            Collections.sort(list);
            long largest = list.get(n - 1);
            long secondLargest = list.get(n - 2);
            sum -= largest;
            list.remove(n - 1);
            if (list.contains(sum - largest))
                list.remove(sum - largest);
            else {
                sum -= secondLargest;
                list.remove(n - 2);
                if (sum != secondLargest) {
                    out.println(-1);
                    continue;
                }
            }
            for (long elem : list)
                out.print(elem + " ");
            out.println();
        }
        out.close();
    }

    // Shuffle and sort array
    static void shuffleAndSort(int[] arr) {
        for (int i = 0; i < arr.length; ++i) {
            int random_index = (int) (Math.random() * arr.length);
            int temp = arr[i];
            arr[i] = arr[random_index];
            arr[random_index] = temp;
        }
        Arrays.sort(arr);
    }

    // Fast IO - Adapted from SecondThread's template
    static class FastScanner {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; ++i) a[i] = nextInt();
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; ++i) a[i] = nextLong();
            return a;
        }
    }
}