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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) {
        FastReader scanner = new FastReader();
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            int n = scanner.nextInt();
            ArrayList<Integer> arrayList = new ArrayList<>(n + 2);
            for (int j = 0; j < n + 2; j++) {
                arrayList.add(scanner.nextInt());
            }
            Collections.sort(arrayList);
            long sum = 0;
            for (int j = 0; j < n + 1; j++) {
                sum += arrayList.get(j);
            }
            int indexOfX = -1;
            for (int j = 0; j < n + 1; j++) {
                long protOfSum = sum - arrayList.get(j);
                if (protOfSum == arrayList.get(arrayList.size() - 1)) {
                    indexOfX = j;
                    break;
                }
            }

            if (indexOfX == -1) {
                sum -= arrayList.get(arrayList.size() - 2);
                if (sum == arrayList.get(arrayList.size() - 2)) {
                    for (int j = 0; j < n; j++) {
                        System.out.print(arrayList.get(j) + " ");
                    }
                } else {
                    System.out.println(-1);
                }
            } else {
                if (indexOfX == arrayList.size() - 1) {
                    for (int j = 0; j < n; j++) {
                        System.out.print(arrayList.get(j) + " ");
                    }
                } else {
                    for (int j = 0; j < n + 1; j++) {
                        if (j == indexOfX) {
                            continue;
                        }
                        System.out.print(arrayList.get(j) + " ");
                    }
                }
                System.out.println();
            }
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                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());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}