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 <cmath>
#include <algorithm>
#include <utility>
#include <iostream>
#include <fstream>
#include <vector>
#include <set>
#include <cstring>

using namespace std;

int main() {

    #ifndef ONLINE_JUDGE
        ifstream cin("a.in");
        ofstream cout("a.out");
    #endif

    int t;
    cin >> t;
    
    while (t--) {
        int n, m;
        cin >> n;
        m = n + 2;
        vector<long long> v(m);

        for (int i = 0; i < m; i++) {
            cin >> v[i];
        }

        sort(v.begin(), v.end());

        long long sum = 0;
        bool found = false;

        for (int i = 0; i < n; i++) {
            sum += v[i];
        }

        if (sum == v[n]) {
            found = true;
            for (int i = 0; i < n; i++) {
                cout << v[i] << ' ';
            }

            cout << "\n";
        }

        sum += v[n];

        for (int i = 0; i < m - 1 && !found; i++) {
            if (sum - v[i] == v[m - 1]) {
                found = true;
                for (int j = 0; j < m - 1; j++) {
                    if (i != j) {
                        cout << v[j] << ' ';
                    }
                }

                cout << "\n";
            }
        }

        if (!found) {
            cout << "-1\n";
        }
    }

    return 0;
}