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
                             

*******************************************************************************/

//===================================================================================================================//
#include<bits/stdc++.h>                                                                                              //                                                                                   
using namespace std;                                                                                                 //
typedef long long ll;                                                                                                //
typedef unsigned long long ul;                                                                                       //
#define to_lower(x)  transform(x.begin(), x.end(), x.begin(), ::tolower)                                             //
#define to_upper(x)  transform(x.begin(), x.end(), x.begin(), ::toupper)                                             //
#define Clock            clock_t tStart = clock()                                                                    //
#define FastIO           ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr)                            //
#define Freopen          freopen("INPUT.txt", "r", stdin); freopen("OUTPUT.txt", "w", stdout)                        //
#define Runtime          fprintf(stderr, "\n>> Runtime: %.10fs\n", (double) (clock() - tStart) / CLOCKS_PER_SEC)     //
#define pi acos(-1)                                                                                                  //
#define ll long long                                                                                                 //
#define ull unsigned long long                                                                                       //
#define vec vector<ll>                                                                                               //
#define f1(x,n) for(i=x;i<n;i++)                                                                                     //
#define input  ll n;cin>>n;ll ar[n];for(i=0;i<n;i++)cin>>ar[i];                                                      //
#define test   ll ttt;cin>>ttt;while(ttt--)                                                                          //
#define faster  ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);                                                 //
#define faster2 ios_base::sync_with_stdio(0);                                                                        //
#define en '\n'                                                                                                      //
#define eps 1e-12                                                                                                    //
#define pb push_back                                                                                                 //
// #define loop(n) for(long long i=0;i<n;i++);                                                                       //
#define print(v) for(auto u:v)cout<<u<<" ";                                                                          //
#define mem(a,b) memset(a, b, sizeof(a) )                                                                            //
//#define loop(i, y)     for(int i=0; i<int(y); i++)                                                                 //
#define fraction() cout.unsetf(ios::floatfield); cout.precision(10); cout.setf(ios::fixed,ios::floatfield);          //
#define MAX              (10000007)                                                                                  //
//================================================================================================================== //
//==========================================Prime number ==================

const ll range=1e7+123;
vec vv;
bitset<range>prime;
void sieve()
{
   prime[0]=1;prime[1]=1;
   for(ll i=2;i<=range;i++)
   {
    if(prime[i]==0)
    {
      for(ll j=i*i;j<=range;j+=i)prime[j]=1;
    }
   }
  vv.pb(2);
  for(ll i=3;i<=range;i+=2)if(prime[i]==0)vv.pb(i);
}
//***************************************Sieve*********************
void Main()
{
    int n;
    cin>>n;
    n+=2;
    int ar[n];
    for(int i=0; i<n; i++)
        cin>>ar[i];
    sort(ar,ar+n);
    ll sum=0;
    for(int i=0; i<n-2; i++)
        sum+=ar[i];
   
   if(sum==ar[n-1] or sum==ar[n-2])
   {
     for(int i=0;i<n-2;i++)cout<<ar[i]<<" ";
      cout<<endl;
   }
  else
  { 
     bool bol=false;
     int keep;
     sum=0;
    for(int i=0; i<n-1; i++)
        sum+=ar[i];
     for(int i=0;i<n-1;i++)
     {
       if(sum-ar[i]==ar[n-1])
         {keep=i;bol=true;break;}
     }
     if(bol)
     {
       
      for(int i=0;i<n-1;i++)
      {
         if(i==keep)continue;
         cout<<ar[i]<<" ";
      }cout<<endl;

     }
     else cout<<-1<<endl;
  }


}
int main()
{

    FastIO;
#ifndef ONLINE_JUDGE
    Clock;
    Freopen;
#endif
//..................mainfunction...............
   //sieve();
   test{Main();}
    //Main();
   

//....................end_the mainfunction.......
#ifndef ONLINE_JUDGE
    Runtime;
#endif

}