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.*;
import java.lang.*;
import java.io.*;

// Created by @thesupremeone on 10/04/21
public class D {
    BufferedReader in;
    BufferedWriter out;
    StringTokenizer st;
    boolean onlineJudge;

    // My Solution
    void solve() throws IOException {
        int t = getInt();
        while (t-->0){
            int n = getInt();
            int[] a = getInts(n+2);
            PriorityQueue<Integer> priorityQueue = new PriorityQueue<>(Comparator.reverseOrder());
            long totalSum = 0, sum = 0;
            for (int e : a) {
                totalSum += e;
                priorityQueue.add(e);
            }
            int x = -1;
            int highest = priorityQueue.poll();
            int secondHighest = priorityQueue.poll();
            if(totalSum-highest-secondHighest==secondHighest){
                x = highest;
                sum = secondHighest;
            }else {
                for (int e : a) {
                    if (e != highest && totalSum - e - highest == highest) {
                        x = e;
                        sum = highest;
                        break;
                    }
                }
            }
            if(x==-1){
                out.write("-1\n");
            }else {
                for (int e : a) {
                    if (e == sum) {
                        sum = -1;
                        continue;
                    }
                    if (e == x) {
                        x = -1;
                        continue;
                    }
                    out.write(e + " ");
                }
                out.write("\n");
            }
        }
    }
    // Handling CodeExecution
    public static void main(String[] args) throws Exception {
        new D().run();
    }
    void run() throws IOException {
        onlineJudge = isOnlineJudge();
        // Defining Input Streams
        if (onlineJudge) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new BufferedWriter(new OutputStreamWriter(System.out));
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new BufferedWriter(new FileWriter("output.txt"));
        }
        // Running Logic
        solve();
        out.flush();
        // Run example test cases
        if (!onlineJudge) {
            BufferedReader output = new BufferedReader(new FileReader("output.txt"));
            BufferedReader answer = new BufferedReader(new FileReader("answer.txt"));
            StringBuilder outFile = new StringBuilder();
            StringBuilder ansFile = new StringBuilder();
            String temp;
            while ((temp = output.readLine()) != null)
                outFile.append(temp.trim());
            while ((temp = answer.readLine()) != null)
                ansFile.append(temp.trim());
            if (outFile.toString().equals(ansFile.toString()))
                System.out.println("Test Cases Passed!!!");
            else
                System.out.println("Failed...");
        }
    }
    // Checks whether the code is running on OnlineJudge or LocalSystem
    boolean isOnlineJudge() {
        try {
            return System.getProperty("ONLINE_JUDGE")!=null
                    || System.getProperty("LOCAL")==null;
        } catch (Exception e) {
            return true;
        }
    }
    // Some functions
    void print(String... s) throws IOException {
        for (String value : s) out.write(value);
    }
    void println(String... s) throws IOException{
        print(s);
        out.newLine();
    }
    String getLine() throws IOException{
        return in.readLine();
    }
    String getToken() throws IOException{
        if(st==null || !st.hasMoreTokens())
            st = new StringTokenizer(getLine());
        return st.nextToken();
    }
    int getInt() throws IOException {
        return Integer.parseInt(getToken());
    }
    long getLong() throws IOException {
        return Long.parseLong(getToken());
    }
    int[] getInts(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = getInt();
        return a;
    }
    long[] getLongs(int n) throws IOException {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = getLong();
        return a;
    }
    int[][] getIntMat(int n, int m) throws IOException {
        int[][] mat = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                mat[i][j] = getInt();
        return mat;
    }
    char[][] getCharMat(int n, int m) throws IOException {
        char[][] mat = new char[n][m];
        for (int i = 0; i < n; i++) {
            String s = getLine();
            for (int j = 0; j < m; j++)
                mat[i][j] = s.charAt(j);
        }
        return mat;
    }
}