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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class CorruptedArray {

	

	static class Fs{
		private BufferedReader reader;
		private StringTokenizer stt;
 
		public Fs() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}
 
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				return null;
			}
		}
 
		public String nextString() {
			while (stt == null || !stt.hasMoreTokens()) {
				stt = new StringTokenizer(nextLine());
				
			}
			return stt.nextToken();
		}
 
		public int nextInt() {
			return Integer.parseInt(nextString());
		}
 
		public long nextLong(){ return Long.parseLong(nextString()); }
	}

	
	static Fs scan = new Fs();
	
	
	public static void merge(long[] arr,int start,int end) {
		long[] temp=new long[end-start+1];
		
		int index=0,l=start,middle=(start+end)/2,r=middle+1;
		
		while(l<=middle && r<=end) {
			if(arr[l]<=arr[r]) temp[index++]=arr[l++];
			else temp[index++]=arr[r++];
		}
		
		while(l<=middle) {
          temp[index++]=arr[l++];
		}
		
		while(r<=end) {
	          temp[index++]=arr[r++];
			}
		
		for(int i=0;i<temp.length;i++) arr[i+start]=temp[i];
	}
	
	public static void sort(long[] arr,int start,int end) {
		if(start<end) {
			int middle=(start+end)/2;
			sort(arr,start,middle);
			sort(arr,middle+1,end);
			merge(arr,start,end);
		}
	}
	
	
		static int binarySearch(long arr[], int l, int r, long x)
		{
			if (r >= l) {
				int mid = l + (r - l) / 2;

				if (arr[mid] == x)
					return mid;
				if (arr[mid] > x)
					return binarySearch(arr, l, mid - 1, x);

				return binarySearch(arr, mid + 1, r, x);
			}
			return -1;
		}


	
	public static void main(String[] args) {
		int t=scan.nextInt();
		int z=0;
		while(z<t) {
			
			int n=scan.nextInt();
			long[] b= new long[n+2];
			long[] a=new long[n];
			for(int i=0;i<n+2;i++)
			{
				b[i]=scan.nextLong();
			}
	        sort(b,0,b.length-1);
	        long sum=0;
	        for(int i=0;i<n;i++) {
	        	a[i]=b[i];
	        	sum+=b[i];
	        	
	        }
	        
	        if(sum>b[n+1]) {
	        	System.out.println(-1);
	        	
	        }
	        else if(sum==b[n]||sum==b[n+1]) {
	        	for(int i=0;i<n;i++) System.out.print(a[i]+" ");
        		System.out.println();
	        }
	        else {
	        	long diff=b[n+1]-sum;
	        	long x = b[n]-diff;
	        	int ind=binarySearch(b,0,n-1,x);
	        	if(ind==-1) System.out.println(ind);
	        	else {
	        		a[ind]=b[n];
	        		for(int i=0;i<n;i++) System.out.print(a[i]+" ");
	        		System.out.println();
	        	}
	        }
	       
			z++;
		}
		
	
	

	}

}