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;
#define ll long long

int main()
{
   ll t;
   cin>>t;
   while(t--)
   {
       ll n,sum=0;
       cin>>n;

       n=n+2;
       map<ll,ll> mp;
       ll arr[n],i,a,b,f=0,j;
       for(i=0;i<n;i++)
       {
         cin>>arr[i];
         mp[arr[i]]++;
         sum=sum+arr[i];
       }
       sort(arr,arr+n);

       for(i=0;i<n;i++)
       {
          sum=sum-arr[i];
          if(sum%2==0)
          {
              a=sum/2;
              if(a==arr[i])
              {
                  if(mp[a]>=2)
                  {
                      b=arr[i];
                      f=1;
                      break;
                  }
              }
              else if(mp[a]>=1)
              {
                   b=arr[i];
                   f=1;
                   break;
              }
            }
          sum=sum+arr[i];
       }

       ll g=0,h=0;
       if(f==0)
        cout<<-1<<endl;
       else
       {
           for(i=0;i<n;i++)
           {
                if(a==arr[i] && g==0)
                {
                    g=1;
                    continue;
                }
                else if(b==arr[i] && h==0)
                {
                    h=1;
                    continue;
                }
                else
                    cout<<arr[i]<<" ";
            }
            cout<<endl;
       }

   }
   return 0;
}