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>
typedef long long int ll;
typedef unsigned long long int ull;
#define N 1010100
#define inf 1e9

#define loop(x, n, r) for(int i = x; i < n; i += r)

#define pb push_back
#define pp pair<int, int>

using namespace std;

int main(){
    ios::sync_with_stdio(0); cin.tie(0);
    int T = 1;
    cin >> T;
    while(T--){
        int n;
        cin >> n;
        vector<int> b(n + 2);
        loop(0, n + 2, 1){
            cin >> b[i];
        }
        sort(b.rbegin(), b.rend());
        ll sum = 0;
        loop(1, n + 2, 1){
            sum += b[i];
        }
        vector<ll> sums(n + 2);
        loop(1, n + 2, 1){
            sums[i] = sum - b[i];
            // cout << sums[i] << ' ';
        }
        int remove_index = -1;
        loop(1, n + 2, 1){
            if(sums[i] == b[0]){
                remove_index = i;
                break;
            }
        }
        // cout << remove_index << '\n';
        if(remove_index == -1){
            if(sum - b[1] == b[1]){
                loop(2, n + 2, 1){
                    if(i != remove_index)
                        cout << b[i] << ' ';
                }
            }
            else{
                cout << -1 << '\n';
                continue;
            }
            // }
            // loop(2, n + 2, 1){
            //     if(sums[i] - b[1] == b[1]){
            //         remove_index = i;
            //         break;
            //     }
            // }
            // if(remove_index == -1){
            //     cout << -1 << '\n';
            //     continue;
            // }
            // else{
            //     loop(2, n + 2, 1){
            //         if(i != remove_index)
            //             cout << b[i] << ' ';
            //     }
            // }
        }
        else{
            loop(1, n + 2, 1){
                if(i != remove_index)
                    cout << b[i] << ' ';
            }
        }
        cout << '\n';
    }
    return 0;
}