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.*;


public class Foobar {
	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;
		}
	} 
static void Input(){

   try {
    FileOutputStream output=new FileOutputStream("output.txt");
    PrintStream out=new PrintStream(output);
    //Diverting the output stream into file "temp.out".Comment the below line to use console
    System.setOut(out);
    
    InputStream input=new FileInputStream("input.txt");
    //Diverting the input stream into file "temp.in".Comment the below line to use console
    System.setIn(input);
    
   } catch (FileNotFoundException e) {
    e.printStackTrace();
   }
}



public static void main(String args[]) throws Exception
{
//Input();
FastReader sc=new FastReader();
int t=sc.nextInt();
for (int test=0;test<t;test++){
	int n=sc.nextInt()+2;
	long arr[]=new long[n];
	long max1=-1;
	long max2=-1;
	int index1=-1;
	int index2=-1;
	for(int i=0;i<n;i++){
		arr[i]=sc.nextInt();
		if(arr[i]>max1){
			max1=arr[i];
			index1=i;
		}
	}
	for(int i=0;i<n;i++){
		if(arr[i]>max2 && i!=index1){
			max2=arr[i];
			index2=i;
		}
	}
	long sum1=0;
	long sum2=0;
	for(int i=0;i<n;i++){
		if(i!=index1){
			sum1+=arr[i];
		}
		if(i!=index2){
			sum2+=arr[i];
		}
	}
	int flag=0;
	int index3=-1;
	int index4=-1;
	for(int i=0;i<n;i++){
		if((sum1-arr[i])==arr[index1] && i!=index1){
			flag=1;
			index3=i;
			index4=index1;
			break;
		}
		if((sum2-arr[i])==arr[index2] && i!=index2){
			flag=1;
			index3=i;
			index4=index2;
			break;
		}
	}
	if(flag==0){
		System.out.print("-1");
	}
	else{
		for(int i=0;i<n;i++){
			if(i!=index3 && i!=index4){
			System.out.print(arr[i]+" ");
		}
		}
	}
	System.out.println("");
	

}
}
}