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:
/*
                                    بسم الله الرحمن الرحيم
                وَاتَّقُوا يَوْمًا تُرْجَعُونَ فِيهِ إِلَى اللَّهِ ۖ ثُمَّ تُوَفَّىٰ كُلُّ نَفْسٍ مَّا كَسَبَتْ وَهُمْ لَا يُظْلَمُونَ
*/
#include <iostream>
#include <bits/stdc++.h>
#include<map>


using namespace std;
void init(){
    cin.tie(0);
    cin.sync_with_stdio(0);
}

   int main()
{
    init();
    long long t;
    cin >> t;
    while(t--)
    {
      long long n;
      cin >> n;
      long long arr[n+2],brr[n+2];
      map<long long , long long > mp;
      for(int i = 0 ; i < n+2 ;i ++)
      {
          cin >> arr[i];
          brr[i]=arr[i];
          mp[arr[i]]++;
      }
      sort(arr,arr+n+2);
      long long c=0;
      for(int i=0;i<n+2;i++)
      {
          if(arr[i]==brr[i])c++;
      }
      if(c==n+2)c=1;
      else c=0;
      long long l=0,r=0,sum=0,f=0;
                            long long e=-1;

      for(int i =0;i<n;i++)
      {
          sum +=arr[i];
      }
       if(sum==arr[n]||sum==arr[n+1])
       {
           for(int i=0;i<n;i++)
            cout <<arr[i]<<" ";
            cout <<"\n";
            continue;
       }
          else
          {
              sum+=arr[n];

                      for(int i=0;i<n+1;i++)
                      {
                          if(arr[i]==sum-arr[n+1])e=i;

                      }
          }
                 if(e==-1)
                 {
                     cout << -1;
                 }
                 else
                 {
                     for(int i = 0 ;i < n + 1 ; i ++)
                     {
                         if(i==e)continue;
                         else cout << arr[i]<<" ";
                     }
                 }


      cout << "\n";
    }
}