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<stdc++.h>
// #include<stdlib>
#include<iostream>
#include<map>
#include<vector>
#include<unordered_map>
#include<string>
#include<algorithm>
#include<set>
#include<numeric>
using namespace std;
typedef long long ll;

void solve() {
	int n;
	cin >> n;
	vector<int> b(n + 2, 0);
	for (int i = 0; i < n + 2; ++i) cin >> b[i];
	// B = 2 * A + x， 枚举x
	multiset<ll> store(b.begin(), b.end());
	ll sum = accumulate(b.begin(), b.end(), 0LL);
	for (auto x : b) {
		store.erase(store.find(x));
		sum -= x;
		if (sum % 2 == 0 && sum <= 2e9 && store.find(sum / 2) != store.end()) {
			store.erase(store.find(sum / 2));
			for (auto t : store) {
				cout << t << " ";
			}
			cout << endl;
			return;
		}
		sum += x;
		store.insert(x);
	}
	cout << -1 << endl;
}

int main()
{
	
// 	freopen("in.txt", "r", stdin);
	int tests;
	cin >> tests;
	while (tests--) {
		solve();
	}
	return 0;
}