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.*;
import java.util.Arrays;
import java.util.StringTokenizer;
 
public class Main {
 
    private static void run(Reader in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        Long[] b = new Long[n + 2];
        long sum = 0;
        for (int i = 0; i < n + 2; i++) {
            b[i] = new Long(in.nextInt());
            sum += b[i];
        }
        Arrays.sort(b);
 
        int x_pos = check(n, b, sum);
        if (x_pos == -1) {
            long tmp = b[n];
            b[n] = b[n + 1];
            b[n + 1] = tmp;
            x_pos = check(n, b, sum);
        }
 
        if (x_pos == -1) {
            out.println(-1);
            return;
        }
 
        for (int i = 0; i <= n; i++) {
            if (x_pos == i) continue;
            out.print(b[i]);
            out.print(' ');
        }
        out.println();
    }
 
    private static int check(int n, Long[] b, long sum) {
        for (int i = 0; i < n + 1; i++) {
            if (b[n + 1] == sum - b[n + 1] - b[i]) {
                return i;
            }
        }
        return -1;
    }
 
    public static void main(String[] args) throws IOException {
        Reader in = new Reader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
 
        int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            run(in, out);
        }
 
        out.flush();
        in.close();
        out.close();
    }
 
    static class Reader {
        BufferedReader reader;
        StringTokenizer st;
 
        Reader(InputStreamReader stream) {
            reader = new BufferedReader(stream, 32768);
            st = null;
        }
 
        void close() throws IOException {
            reader.close();
        }
 
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        String nextLine() throws IOException {
            return reader.readLine();
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
    }
}