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:
//      これを翻訳している間、あなたはあなたの人生のいくつかの貴重な瞬間を無駄にしました
//  DO something instead of nothing

import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


public class Solution {
    static PrintWriter fop = new PrintWriter(System.out);
    



    public static void main(String[] args) {
        FastScanner fsca = new FastScanner();


        int t = fsca.nextInt();
    outer :    while (t-- > 0) {

        int max1 = -1 ;
        int max2 = -1 ;
        int max1in = -1 ;
        int max2in = -1 ;

        int n = fsca.nextInt();
        int a[] = fsca.readArray(n + 2);
        long sum = 0 ;

        for (int i = 0; i < n+2 ; i++) {
            if (a[i] > max1){
                max2 = max1 ;
                max1 = a[i] ;
                max2in = max1in ;
                max1in = i ;
            }
            else if (a[i] > max2){
                max2in = i ;
                max2 = a[i] ;
            }
            sum += a[i] ;
        }

        long tt = sum - max1 - max2 ;
        if (tt == max1 || tt == max2){
            for (int j = 0; j <n+2 ; j++) {
                if (j != max1in && j != max2in)
                    fop.append(a[j] + " ") ;

            }
            fop.append("\n");
            continue  outer;



        }
        else {
            for (int i = 0; i <n+2 ; i++) {
                if (i == max1in)
                    continue ;
                long curr = sum - a[i] - max1 ;
                if (curr == max1){

                    for (int j = 0; j <n +2; j++) {
                        if (j != max1in && j != i)
                            fop.append(a[j] + " ") ;

                    }
                    fop.append("\n");
                    continue  outer;

                }

            }

           fop.append(-1 + "\n") ;


        }







    }





        fop.flush();
        fop.close();


    }
    /*-----------------------------------------------------------------------------------------------------------------------------------------------*/


    static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    ;

    static int gcd(int a, int b) {
        return (b == 0) ? a : gcd(b, a % b);
    }


    static final Random random = new Random();

    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(long[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n);
            long temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }


    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());
        }

        int[][] readMat(int n, int m) {
            int a[][] = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = nextInt();
            return a;
        }

        char[][] readCharMat(int n, int m) {
            char a[][] = new char[n][m];
            for (int i = 0; i < n; i++) {
                String s = next();
                for (int j = 0; j < m; j++)
                    a[i][j] = s.charAt(j);
            }
            return a;
        }


        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;
        }

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

    static void print(int a[], int n) {
        for (int i = 0; i < n; i++)
            fop.append((a[i]) + " ");
        // fop.append("\n") ;
    }

    static void print(long a[], int n) {
        for (int i = 0; i < n; i++)
            fop.append((a[i]) + " ");
        // fop.append("\n") ;
    }
}