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 <algorithm>
#define ll long long
#define over "\n"

using namespace std;

void fun()
{
    ll n;
    cin >> n;
    vector<ll> b(n + 2);
    ll a;
    ll answer = 0;
    for (ll i = 0; i < n + 2; i++)
    {
        cin >> a;
        b[i] = a;
    }
    sort(b.begin(), b.end());
    ll sum = 0;
    for (ll i = 0; i < n; i++)
    {
        sum += b[i];
    }
    if (sum == b[n + 1] || sum == b[n])
    {
        for (ll i = 0; i < n - 1; i++)
        {
            cout << b[i] << " ";
        }
        cout << b[n - 1] << over;
        answer = 2;
    }
    else
    {
        ll checker = sum + b[n] - b[n + 1];
        for (ll x = 0; x < n; x++)
        {
            if (b[x] == checker)
            {
                b[x] = b[n];
                for (ll i = 0; i < n - 1; i++)
                {
                    cout << b[i] << " ";
                }
                cout << b[n - 1] << over;
                answer = 2;
                break;
            }
        }
    }
    if (answer == 0)
    {
        cout << -1 << over;
    }
}

int main()
{
    ll t;
    cin >> t;
    while (t--)
    {
        fun();
    }
}