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
#define inf 0x3f3f3f3f

ll bs(ll arr[], ll x,ll start, ll end){
    // cout << x << " "<< start << " " << end << endl ;
    if(start>end)
        return -1;
    
    ll mid = (start+end)/2 ;
    if(arr[mid]==x){
        return mid ;
    }else if(arr[mid]>x){
        return bs(arr,x,start,mid-1);
    }else{
        return bs(arr,x,mid+1,end);
    }
}

int main(){
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    std::cout << std::fixed << std::setprecision(0);
    int testCases ;
    cin >> testCases ;
    while(testCases--){
        ll n ; 
        cin >> n ;
        ll arr[n+2];
        ll sumn =0 ;
        // cout << "start\n" ;
        for(ll i =0 ; i<n+2 ; i++){
            cin >> arr[i] ;
            sumn = sumn + arr[i] ;
        }
        // cout << "x0\n" ;
        sort(arr,arr+n+2) ;
        // cout << "x1\n";
        sumn = sumn - (arr[n] + arr[n+1]) ;
        // cout<<"x2\n";
        // cout << "sumn is "<< sumn << endl ;
        // cout<< "x3\n"; 
        // for(int i=0 ; i<n+2 ; i++){
        //     cout<<arr[i]<<" ";
        // }
        // cout<<endl ;
        if( sumn == arr[n] ){
            // cout << "hi"<<endl ;
            for(ll i=0 ; i<n ; i++){
                cout << arr[i] <<" " ;
            }
            cout << endl ;
            continue ;
        }
        // cout<<"x2\n";
        sumn = sumn + arr[n] ;
        // cout<<"x3\n";
        ll x = sumn - arr[n+1] ;

        if(x<0){
            // cout << "hi3"<<endl ;
            cout << -1 << endl ;
            continue ;
        }
        // cout << x <<" " << 0 << " " << n << endl ;
        ll ind = bs(arr,x,0,n);
        // cout << "hi3.5"<<endl ;
        // cout << "ind is "<< ind <<endl ;
        if(ind==-1){
            // cout << "hi4"<<endl ;
            cout << -1 <<endl ;
            continue ;
        }
        // cout << "hi5"<<endl ;
        for(ll i=0 ; i<n+1 ; i++){
            if(i==ind)
                continue ; 
            cout << arr[i] << " ";
        }
        cout << endl ;
    }
    return 0 ;
}