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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {

	void run() throws Exception {
		int cnt_tests = nextInt();
		for (int test = 0; test < cnt_tests; test++) {
			solve();
		}
	}
	static int[] m = new int[200_003];
	private void solve() throws Exception {
		int n = nextInt() + 2;

		long sum0 = 0;
		long max1 = 0;
		long max2 = 0;
		
		for(int i = 0; i < n; i++) {
			m[i] = nextInt();
			sum0 += m[i];
			if (max1 < m[i]) {
				max2 = max1;
				max1 = m[i];
			} else {
				max2 = Math.max(max2,  m[i]);
			}
		}

		StringBuilder sb = new StringBuilder();
		Arrays.sort(m, 0, n/4);

		long x = -1;
		long y = -1;
		{
			if (sum0 - max1 - max2 == max2) {
				// x is max1?
				x = max1;
				y = max2;
			} else {
				// max1 is sum
				x = sum0 - max1 - max1;
				y = max1;
			}
		}

		boolean x_skipped  = false;
		boolean y_skipped  = false;
		boolean added = false;
		for(int i = 0; i < n; i++) {
			if(m[i] == x && !x_skipped) {
				x_skipped = true;
				continue;
			} if(m[i] == y && !y_skipped) {
				y_skipped = true;
				continue;
			} else {
				if (added) sb.append(" ");
				added = true;
				sb.append(m[i]);
			}
		}
		if (x_skipped && y_skipped) {
			out.println(sb);
		} else {
			out.println(-1);
		}
		
	}

	public static void main(String[] args) throws Exception {
		Main instance = new Main();
		instance.initStreams();
		instance.run();
		instance.closeStreams();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

	void initStreams() throws FileNotFoundException {
		if (new File("input.txt").exists()) {
			try {
				System.setIn(new FileInputStream("input.txt"));
			} catch (FileNotFoundException e1) {
				e1.printStackTrace();
			}
		}
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
	}

	void closeStreams() throws IOException {
		in.close();
		out.close();
	}

	String nextString() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextString());
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextString());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextString());
	}
}