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:
//package april2021;
import java.util.*;



import java.io.*;
public class Q1 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn=new Scanner(System.in);
		int t=scn.nextInt();
		while(t-->0) {
		//	System.out.println();
			int n=scn.nextInt();
			long[] arr=new long[n+2];
			long[] ans=new long[n];
			long sum=0;
			for(int i=0; i<n+2; i++) {
				arr[i]=scn.nextLong();
				sum+=arr[i];
			}
			HashSet<Long> even=new HashSet<>();
			HashSet<Long> odd=new HashSet<>();
			for(int i=0; i<n+2; i++) {
				if(arr[i]%2==0) {
					even.add(arr[i]);
				}
				else {
					odd.add(arr[i]);
				}
			}
			HashMap<Long,Integer> map1=new HashMap<>();
			HashMap<Long,Integer> map=new HashMap<>();
			for(int i=0; i<n+2; i++) {
				map.put(arr[i], i);
			}
			for(int i=0; i<(n+2); i++) {
				map1.put(arr[i], map1.getOrDefault(arr[i], 0)+1);
			}
			if(sum%2==0) {
				long num=-1;
				long half=-1;
				for(Long y: even) {
					long sum1=sum;
					sum=sum-y;
					
					half=sum/2;
					sum=sum1;
					if(y==half) {
						if(map1.get(y)>1) {
							num=y;
							break;
						}
						else {
							break;
						}
					}
					if(map.containsKey(half)==true) {
						num=y;
						break;
					}
				}
				if(num==-1) {
					System.out.println(-1);
				}
				else {
					int ind=map.get(num);
					int k=0;
					int is=0;
				/*	if(map1.get(half)>1) {
						ans[k]=half;
						is=1;
						k++;
					}*/
					
					for(int i=0; i<n+2; i++) {
						if(i==ind) {
							
						}
						else if(is==0 && arr[i]==half && i!=ind) {
							is=1;
						}
						else {
							if(k<n) {
								ans[k]=arr[i];
								k++;
							}
						}
					}
					Arrays.sort(ans);
					display(ans);
				}
			}
			else {
				long num=-1;
				long half=-1;
				for(Long y: odd) {
					long sum1=sum;
					sum=sum-y;
					
					half=sum/2;
					sum=sum1;
					if(y==half) {
						if(map1.get(y)>1) {
							num=y;
							break;
						}
						else {
							break;
						}
					}
					if(map.containsKey(half)==true) {
						num=y;
						break;
					}
				}
				if(num==-1) {
					System.out.println(-1);
				}
				else {
					int ind=map.get(num);
					int k=0;
					int is=0;
					/*if(map1.get(half)>1) {
						ans[k]=half;
						is=1;
						k++;
					}*/
					
					for(int i=0; i<n+2; i++) {
						if(i==ind) {
							
						}
						else if(is==0 && arr[i]==half) {
							is=1;
						}
						else {
							if(k<n) {
								ans[k]=arr[i];
								k++;
							}
						}
						
					}
					Arrays.sort(ans);
					display(ans);
				}
			}
			
		}

	}
	private static void display(long[] ans) {
		for(int i=0; i<ans.length; i++) {
			System.out.print(ans[i]+" ");
		}
		System.out.println();
	}

}