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 uo{
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int testcases = Integer.parseInt(st.nextToken());
		for(int lmn=0;lmn<testcases;lmn++){
			st = new StringTokenizer(br.readLine());
			int n = Integer.parseInt(st.nextToken());
			
			st = new StringTokenizer(br.readLine());
			int[] a = new int[n+2];
			n+=2;
			int max = Integer.MIN_VALUE;
			int smax = Integer.MIN_VALUE;
			int maxidx = -1;
			long sum = 0;
			int scdidx = -1;
			HashSet<Integer> set = new HashSet<Integer>();
			for(int i=0;i<n;i++){
				a[i] = Integer.parseInt(st.nextToken());
				sum+=a[i];
				if(a[i]>=max){
					int temp = max;
					scdidx = maxidx;
					max = a[i];
					smax = temp;
					maxidx = i;
				}
				else if(a[i]>smax){
					smax = a[i];
					scdidx = i;
				}
				set.add(a[i]);
			}
			int ans = -1;
			sum-=max;
			for(int i=0;i<n;i++){
				if(i!=maxidx && sum-a[i]==max){
					ans = i;
					break;
				}
			}
			if(ans==-1){
				sum+=max;
				sum-=smax;
				for(int i=0;i<n;i++){
					// System.out.println(i+" "+scdidx+" "+a[i]+" "+smax+" "+sum);
				if(i!=scdidx && sum-a[i]==smax){

					ans = i;
					break;
				}
				}
				if(ans==-1){
					System.out.println(-1);
				}
				else{
					for(int i = 0;i<n;i++){
						if(i==ans || i==scdidx){}
							else{
							System.out.print(a[i]+" ");
						}
					}
					System.out.println();
				}
			}
			else{
				
				for(int i = 0;i<n;i++){
					if(i==ans || i==maxidx){}
						else{
						System.out.print(a[i]+" ");
					}
				}
				System.out.println();
			}

		}
		
		
	}
}