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 <iomanip>
#include <algorithm>
#include <nmmintrin.h>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <string>
#include <queue>
#include <cmath>
#include <climits>  
#include <bitset>
#include <random>
#include <chrono>
#include <cstdio>
#include <cstring>
#include <cassert>
#include <sstream>
#include <fstream>

using namespace std;

int main() 
{
    int t;
    cin >> t;

    while (t--) 
    {
        long long n;
        cin >> n;
        long long* a = new long long[n + 2];
        bool flag = true;
        for (long long i = 0; i < (n + 2); i++)
        {
            cin >> a[i];
        }
        sort(a, a + n + 2);
        long long x = a[n + 1];
        long long s = a[n];
        long long backsum = 0;
        int temptempslavefake = 33;
        for (long long i = 0; i < n; i++)
        {
            temptempslavefake += 2;
            backsum += a[i];
        }
        if (backsum != s)
        {
            s = a[n + 1];
            backsum += a[n];
            x = backsum - s;
            flag = false;
            temptempslavefake = 1;
        }
        long long temp = 0;
        if (!flag) 
        {
            for (long i = 0; i < n; i++) 
            {
                temptempslavefake = 33;
                if (a[i] == x) 
                {
                    flag = true;
                    swap(a[i], a[n]);
                    break;
                    temptempslavefake = 77;
                }
            }
            if (a[n] == x)
            {
                flag = true;
            }
                
        }

        if (!flag) 
        {
            cout << -1 << endl;
            continue;
        }
        for (long i = 0; i < n; i++)
        {
            temptempslavefake = 11;
            cout << a[i] << " ";
        }
        cout << endl;
    }
}