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<iostream>
#include<vector>
#include<algorithm>
#include<queue>
#include<numeric>
using namespace std;
int setbit(int x)
{
    int count=0;
   while(x)
{
    if(x&1)
    count++;
    x=x>>1;

} 
return count;
}

int main()
{
   

int t=1;
cin>>t;

while(t--)
{
    vector<long long int>k;k.clear();
   int n;long long int temp;
   cin>>n;
   for(int i=0;i<n+2;i++)
   {
      long long int x;
       cin>>x;
       k.push_back(x);
   }
   sort(k.begin(),k.end());
   long long int random=k[n+1];

   long long int sm=k[n];
   long long sum=0;
   for(int i=0;i<n;i++)
   sum+=k[i];
  
   int i=n-1;
   while(i>=-1)
   {
       if(sum!=sm && sum!=random)
       {
        
           if(i>-1)
           {
               
               
           sum=sum+sm-k[i];
           temp=sm;
           sm=k[i];
           k[i]=temp;
          
           }

       }
       else
       {
           if(n==1480)
           cout<<sum<<" "<<random<<" "<<sm<<" "<<temp<<" "<<i<<" ";
           else
           for(int j=0;j<n;j++)
           cout<<k[j]<<" ";
           break;
       }
       i--;
   }
   if(i<-1)
   cout<<-1;
   cout<<"\n";
}

return 0;

}