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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int main()
{
		int t;
		cin>>t;
		while(t--)
		{
			int n;
			cin>>n;
			vector<int>b,a;
			long long int s=0;
			for(int i=0;i<n+2;i++)
			{
				int x;
				cin>>x;
				b.push_back(x);
				s=s+x;
			}
			long long int s1=0;
			sort(b.begin(),b.end());
			for(int i=0;i<n;i++)
			{
				s1=s1+b[i];
			}
			int k=-1;
			if(s-s1-b[n]==s1)
			{
		 	for(int i=0;i<n;i++)
		 		a.push_back(b[i]);
		 		a.push_back(b[n+1]);
			}
			else if(s-s1-b[n+1]==s1)
			{
				for(int i=0;i<n;i++)
		 		a.push_back(b[i]);
		 		a.push_back(b[n]);
			}
			else
			{
				for(int i=0;i<n;i++)
				{
					if(s1-b[i]+b[n]==b[n+1] || s1-b[i]+b[n+1]==b[n])
					{
						k=i;
						break;
					}
				}
			}
//			cout<<k<<endl;
				if(k==-1 && a.size()==0)
				cout<<-1;
				else if(k==-1 && a.size()>0)
				{
					for(int i=0;i<n;i++)
					cout<<a[i]<<" ";
				}
				else{
					if(s1-b[k]+b[n]==b[n+1])
					{
						for(int i=0;i<n+2;i++)
						{
							if(i==k || i==n+1)
							continue;
							else
							a.push_back(b[i]);
						}
					}
					else{
						for(int i=0;i<n+2;i++)
						{
							if(i==k || i==n)
							continue;
							else
							a.push_back(b[i]);
						}
					}
					for(int i=0;i<n;i++)
					{
						cout<<a[i]<<" ";
					}
				}
				cout<<endl;
		}
	
	return 0;
}