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>
using namespace std;

typedef long long ll;

int main()
{
    ll t;
    cin >> t;
    while (t--)
    {
        ll n;
        cin >> n;
        vector<ll> b(n + 2);
        set<ll> s;
        ll sum = 0;
        for (ll &i : b)
        {
            cin >> i;
            s.insert(i);
            sum += i;
        }

        sort(b.begin(), b.end());
        sum -= b[n + 1];

        if (sum <= b[n + 1])
        {
            sum -= b[n];
            if (sum == b[n])
            {
                for (ll i = 0; i < n; ++i)
                    cout << b[i] << " ";
                cout << endl;
            }
            else
                cout << "-1" << endl;
        }
        else
        {
            ll diff = sum - b[n + 1];
            if (diff == b[n + 1])
            {
                if (b[n + 1] == b[n])
                {
                    for (ll i = 0; i < n; ++i)
                        cout << b[i] << " ";
                    cout << endl;
                }
                else
                    cout << "-1" << endl;
                continue;
            }
            set<ll>::iterator itr = s.find(diff);
            if (*itr == diff)
            {
                // cout << "here" << diff << endl;
                ll i = 0;
                while (b[i] != diff)
                {
                    cout << b[i] << " ";
                    i++;
                }
                i++;
                while (i <= n)
                {
                    cout << b[i] << " ";
                    i++;
                }
                cout << endl;
            }
            else
            {
                // cout << "there" << endl;
                sum -= b[n];
                if (sum == b[n])
                {
                    for (ll i = 0; i < n; ++i)
                        cout << b[i] << " ";
                    cout << endl;
                }
                else
                    cout << "-1" << endl;
            }
        }
    }
    return 0;
}