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<cstdlib>
#include<queue>
#include<random>
#include<map>
#include<cstring>
#include<string>
#include<unordered_map>
#include<algorithm>
using namespace std;
long long b[200010];
int main() {
	int q;
	cin >> q;

	unordered_map<long long, int> mp;
	while (q--) {
		mp.clear();
		int n;
		cin >> n;
		long long sum = 0;
		for (int i = 0; i < n + 2; i++) {
			cin >> b[i];
			mp[b[i]] = 1;
			sum += b[i];
		}
		sort(b, b + n + 2);
		mp[b[n + 1]] = 0;
		long long x = sum - 2 * b[n + 1], y = sum - 2 * b[n];
		//cout << sum << " " << x << " " << y << endl;
		if (mp[x]) {
			bool flag = true;
			for (int i = 0; i < n + 1; i++) {
				if (flag && b[i] == x) {
					flag = false;
					continue;
				}
				cout << b[i] << " ";
			}
			cout << endl;
		}
		else if (y == b[n + 1]) {
			for (int i = 0; i < n ; i++) {
				cout << b[i] << " ";
			}
			cout << endl;
		}
		else cout << -1 << endl;
	}

	return 0;
}