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.*;
import java.math.*;
 

public final class Solution{

	public static void main(String[] args) throws IOException{
//		Scanner sc=new Scanner(System.in);
		FastReader sc=new FastReader();
		PrintWriter writer=new PrintWriter(System.out);
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt()+2;
			long[] a=new long[n];
			long sum=0, max=a[0], smax=0; int idx1=0, idx2=0;
			for(int i=0;i<n;i++) {
				a[i]=sc.nextLong();
				sum+=a[i];
				if(max<a[i]) {
					max=a[i];
					idx1=i;
				}
			}
			for(int i=0;i<n;i++) {
				if(smax<a[i] && i!=idx1) {
					smax=a[i]; idx2=i;
				}
			}
			int f=0;
			for(int i=0;i<n;i++) {
				if(i!=idx1) {
					if(sum-a[idx1]-a[i]==a[idx1]) {
						idx2=i; f=1; break;
					}
				}
			}
			if(f==0) {
				for(int i=0;i<n;i++) {
					if(i!=idx2) {
						if(sum-a[idx2]-a[i]==a[idx2]) {
							idx1=i; f=1; break;
						}
					}
				}
			}
			if(f==1) {
				for(int i=0;i<n;i++) {
					if(i!=idx1 && i!=idx2)
						writer.print(a[i]+" ");
				}
				writer.println();
			}else writer.println("-1");
			
		}
		
		writer.flush();
		writer.close();
  }
    
  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; 
        } 
    }
   
}