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.io.*;
 

public class SolutionD{
       public static void main(String[] args) throws Exception{
               Fast sc=new Fast();
       StringBuilder sb=new StringBuilder();
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt();
            int[] ar=new int[n+2];
            int[] br=new int[n+2];
            long sum=0;
            for(int i=0;i<n+2;i++){
                ar[i]=sc.nextInt();
            }
            Sort(ar);
            int val=ar[n+1];
            int sval=ar[n];
            for(int i=0;i<n;i++){
                sum+=(long)ar[i];
            }
            if(sum==(long)val || sum==(long)sval){
                for(int i=0;i<n;i++){
                    sb.append(ar[i]+" ");
                }
                sb.append("\n");
            }
            else{
                sum+=(long)ar[n];
                int[] vis=new int[n+1];
                boolean ok=false;
                
                for(int i=0;i<=n;i++){
                    if(sum-(long)ar[i]==val){
                        vis[i]=1;
                        ok=true;
                        break;
                    }
                }
                if(ok){
                    for(int i=0;i<=n;i++){
                       if(vis[i]==0)sb.append(ar[i]+" "); 
                    }
                    sb.append("\n");
                }
                else sb.append("-1"+"\n");
            }
            
         
           
        }
        System.out.println(sb);
    }


static void ReverSort(int[] ar){
    ArrayList<Integer> al=new ArrayList<>();
    for(int i=0;i<ar.length;i++){
        al.add(ar[i]);
    }

    Collections.sort(al);
      int j=0;
    for(int i=al.size()-1;i>=0;i--){

        ar[j]=al.get(i);
        j++;
    }
}
static void Sort(int[] ar){
    ArrayList<Integer> al=new ArrayList<>();
    for(int i=0;i<ar.length;i++){
        al.add(ar[i]);
    }

    Collections.sort(al);
      int j=0;
    for(int i=0;i<al.size();i++){

        ar[j]=al.get(i);
        j++;
     }
  }

 
static int gcd(int a,int b){
    if(b==0) return a;
    else return  gcd(b,a%b);
}
}

class Pair{
    int x, y;
     Pair(int x,int y){
        this.x=x;
        this.y=y;
     }
}

class SortPair implements Comparator<Pair>{

    public int compare(Pair p1, Pair p2){
        return p1.y-p2.y;
    }
}

class Fast{
  BufferedReader br; 
  StringTokenizer st;
  public Fast(){ 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; 
        } 
}