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 <unordered_map>
#include <set>
#include <utility>
#include <queue>
#include <algorithm>
#include <iomanip>
#include <map>
 
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// ░░░░░▄█▄░░▀▀▀▀▀▀▀▀▄░░▀▀▀▀▀▀▀░▄▀░ Gonna cock balls cock balls after school
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using namespace std;
typedef long long ll;
typedef long double ld;
 
//for epic memory
//#define ll int
 
#define INF ll(1e18)
#define SIZE 110
#define MOD 998244353
 
#define s second
#define f first
 
#define loop(i,n) for(ll i=0;i<n;i++)
#define loopone(i,n) for(ll i=1;i<=n;i++)
#define loopb(i,n) for(ll i=n-1;i>=0;i--)
#define loopbone(i,n) for(ll i=n;i>0;i--)

#define sgnl(i) cout<<"\ni'm here with this -> "<<i<<"\n";
 
ll n, m, i, j, x, y, z, k;
char chr;
 
vector<pair<ll,ll>> go = {{-1, 0},{1, 0},{0, -1},{0, 1}};
struct helper{ll a, b, size;};
 
ll zalupa;
string str;

//


char mapa[500][500];


int main(){
    
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cin >> zalupa;
    
    while(zalupa--){
     
        cin >> n;
        
        vector<ll>vec;
        
        loop(i, n+2){
            cin >> x;
            vec.push_back(x);
        }
        
        sort(vec.begin(), vec.end());
        
        ll sums = 0;
        loop(i, n)
            sums += vec[i];
        
       
        if(sums == vec[n]){
            
            loop(i, n)
                    cout << vec[i] << ' ';
            cout << '\n';
            continue;
        }
        
        sums += vec[n];
        
        ll need = sums - vec[n+1];
        if(need < 1){cout << -1 << '\n';continue;}
        
        ll bad = 1;
        ll good_i = 1;
        
        loop(i, n+1)
            if(vec[i] == need)
                bad = 0, good_i = i;
        
        if(bad){cout << -1 << '\n';continue;}
        
        loop(i, n+1)
            if(i != good_i)
                cout << vec[i] << ' ';
        
        
        cout << '\n';
        
       
    }
    return 0;
    
}