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.sql.SQLOutput;
import java.util.Arrays;
import java.util.*;
//import java.util.*;
import java.io.*;

public class D_Corrupted_Array {

    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;
    public D_Corrupted_Array()
    {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }
    public D_Corrupted_Array(String file_name) throws IOException
    {
        din = new DataInputStream(
                new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }
    private byte read() throws IOException
    {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }
    private void fillBuffer() throws IOException
    {
        bytesRead = din.read(buffer, bufferPointer = 0,
                BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }
    public int nextInt() throws IOException
    {
        int ret = 0;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    int n;
    public int checker(long man[],long sum,long max_value,HashMap<Integer,Long> h,int key){


        //Arrays.sort(man);
       // long sum=0;
       /* for(int i=0;i<n;i++){
            sum=sum+man[i];
        }*/
        long max_se_choti=0;
        for(int i=0;i<n+2;i++){
            if(man[i]>max_se_choti&&man[i]<max_value){max_se_choti=man[i];}
            if(i==n+1&&max_se_choti==0){max_se_choti=man[n+1];}
        }
        long simp=sum;
        //sum=sum-man[n]-man[n+1];
        long taka_nahi_bhida_hai1=0;
        long taka_nahi_bhida_hai2=0;
        simp=simp-max_se_choti-max_value;
        if((simp==max_se_choti)||(simp==max_value)){
            for(int i=0;i<n+2;i++){
                if(man[i]==max_se_choti&&taka_nahi_bhida_hai1==0){taka_nahi_bhida_hai1=taka_nahi_bhida_hai1+1;continue;}
                if(man[i]==max_value&&taka_nahi_bhida_hai2==0){taka_nahi_bhida_hai2=taka_nahi_bhida_hai2+1;continue;}
                System.out.print(man[i]+" ");

            }
            System.out.println();
            return -1;
        }
         h.remove(key);
        /*if(sum==man[n+1]){
            for(int i=0;i<n;i++){
                System.out.print(man[i]+" ");

            }
            return -1;
        }*/
        //long sum1;
       /* for(int j=0;j<n;j++){
            if(j>0){
                if(man[j]==man[j-1]){continue;}
            }

            sum1=sum;
            sum1=sum1-man[j]+man[n];
            if(sum1==man[n+1]){
                for(int i=0;i<n+1;i++){
                    if(i==j){continue;}
                    System.out.print(man[i]+" ");

                }
                return -1;
            }


        }*/
       // sum1=sum+man[n]-man[n+1];
        simp=simp+max_se_choti;
        long pyaar_deewana_hota_hai=simp-max_value;
        //int pyara=Arrays.binarySearch(man,0,n,sum1);
         long taka_bhida_hai=0;
        if(h.containsValue(pyaar_deewana_hota_hai)){
            for(int i=0;i<n+2;i++){
                if(man[i]==max_value){continue;}
                if(man[i]==pyaar_deewana_hota_hai&&taka_bhida_hai==0){taka_bhida_hai=taka_bhida_hai+1;continue; }
                System.out.print(man[i]+" ");
            }
            System.out.println();
            return -1;
        }


        System.out.println("-1");
        System.out.println();
        return -1;


    }
    public long nextLong() throws IOException
    {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }
    public static void main(String args[])throws java.lang.Exception{
        D_Corrupted_Array sc=new D_Corrupted_Array();
        // System.out.println("enter the no. of testcases");
        int t=sc.nextInt();
        for(int i=0;i<t;i++){
            int key=0;
            long sum=0;
            long max_value=0;
            D_Corrupted_Array d=new D_Corrupted_Array();
            // System.out.println("enter the value of n");
            d.n=sc.nextInt();
            HashMap<Integer,Long> h=new HashMap<>();
            long array[]=new long[d.n+2];
            for(int j=0;j<d.n+2;j++){
                array[j]=sc.nextLong();
                sum=sum+array[j];
                h.put(j,array[j]);
                if(array[j]>max_value){max_value=array[j];key=j;}


            }

            d.checker(array,sum,max_value,h,key);


        }

    }
}