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.*;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		int t = in.nextInt();
		while(t-- > 0) {
			int n = in.nextInt();
			Integer[] a = new Integer[n+2];
			long sum = 0;
			for(int i = 0; i < a.length; i++) {
				a[i] = in.nextInt();
				sum += a[i];
			}
			Arrays.sort(a);
			boolean bool = false;
			int j = n+1, i = 0;
			for(j = n+1; j >= n; j--) {
				for(i = 0; i <= n+1; i++) {
					if(i == j) {
						continue;
					}
					if(sum - a[i] - a[j] == a[j]) {
						bool = true;
						break;
					}
				}
				if(bool) {
					break;
				}
			}
			
			if(bool) {
				for(int k = 0; k < a.length; k++) {
					if(k != i && k != j)
						System.out.print(a[k] + " ");
				}

				System.out.println();
			}
			
			else {
				System.out.println(-1);
			}
		}
	}	
	
	static long gcd(long a, long b) {
		if (a % b == 0) {
			return b;
		} else {
			return gcd(b, a % b);
		}
	}
	static void reverseArray(int[] a) {
		for (int i = 0; i < (a.length >> 1); i++) {
			int temp = a[i];
			a[i] = a[a.length - 1 - i];
			a[a.length - 1 - i] = temp;
		}
	}
	static int[] intInput(int n, InputReader in) {
		int[] a = new int[n];
		for (int i = 0; i < a.length; i++)
			a[i] = in.nextInt();
		return a;
	}
	static long[] longInput(int n, InputReader in) {
		long[] a = new long[n];
		for (int i = 0; i < a.length; i++)
			a[i] = in.nextLong();
		return a;
	}
	static String[] strInput(int n, InputReader in) {
		String[] a = new String[n];
		for (int i = 0; i < a.length; i++)
			a[i] = in.next();
		return a;
	}
}

class Data {
	int i, v;

	Data(int i, int v) {
		this.i = i;
		this.v = v;
	}
}

class compare implements Comparator<Data> {

	@Override
	public int compare(Data o1, Data o2) {
		return o1.v - o2.v;
	}

}

class InputReader {
	public BufferedReader reader;
	public StringTokenizer tokenizer;

	public InputReader(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
	}

	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	long nextLong() {
		return Long.parseLong(next());
	}

	double nextDouble() {
		return Double.parseDouble(next());
	}

	String nextLine() {
		String str = "";
		try {
			str = reader.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return str;
	}

}