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.*;

public class D {
    static FastReader reader = new FastReader();
    static OutputWriter out = new OutputWriter(System.out);


    public static void main(String[] args) {
        int tests = reader.nextInt();
        outer : for (int test = 1; test <= tests; test++) {
            int n = reader.nextInt();
            List<Integer> arr = new ArrayList<>();
            long sum = 0;
            for(int i = 0; i < n + 2; i++) {
                int cur = reader.nextInt();
                arr.add(cur);
            }
            Collections.sort(arr);
            for(int i = 0; i < arr.size() - 1; i++) sum+=arr.get(i);
            long max = arr.get(arr.size() - 1);
            for(int i = 0; i < arr.size() - 1; i++) {
                long tSum = sum - arr.get(i);
                if (tSum == max) {
                    for(int j = 0; j < arr.size() - 1; j++) {
                        if(j == i) continue;
                        out.print(arr.get(j) + " ");
                    }
                    out.println();continue outer;
                }
            }
            max = arr.get(arr.size() - 2);
            long ts = 0;
            for(int i = 0; i < arr.size() - 2; i++) ts+=arr.get(i);
            if(ts == max) {
                for(int i = 0; i < arr.size() - 2; i++) {
                    out.print(arr.get(i) + " ");
                }
                out.println();
            } else {
                out.println(-1);
            }
        }
        out.flush();
    }


    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;
        }
    }

    public static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(char[] array) {
            writer.print(array);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void print(double[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void print(long[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void println(int[] array) {
            print(array);
            writer.println();
        }

        public void println(double[] array) {
            print(array);
            writer.println();
        }

        public void println(long[] array) {
            print(array);
            writer.println();
        }

        public void println() {
            writer.println();
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void print(char i) {
            writer.print(i);
        }

        public void println(char i) {
            writer.println(i);
        }

        public void println(char[] array) {
            writer.println(array);
        }

        public void printf(String format, Object... objects) {
            writer.printf(format, objects);
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            writer.flush();
        }

        public void print(long i) {
            writer.print(i);
        }

        public void println(long i) {
            writer.println(i);
        }

        public void print(int i) {
            writer.print(i);
        }

        public void println(int i) {
            writer.println(i);
        }

        public void separateLines(int[] array) {
            for (int i : array) {
                println(i);
            }
        }
    }
}