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 Corrupted_Array {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		InputStream inputStream = System.in;

		InputReader in = new InputReader(inputStream);
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

		int t = in.nextInt();
		while (t-- != 0) {
			int n = in.nextInt();
			int[] arr = in.readArray(n + 2);
			int max = Integer.MIN_VALUE;
			int max_idx = -1;
			for (int idx = 0; idx < arr.length; idx++) {
				if (max <= arr[idx]) {
					max = arr[idx];
					max_idx = idx;
				}
			}
			int temp = arr[arr.length - 1];
			arr[arr.length - 1] = max;
			arr[max_idx] = temp;
			max = Integer.MIN_VALUE;
			max_idx = -1;
			for (int idx = 0; idx < arr.length - 1; idx++) {
				if (max <= arr[idx]) {
					max = arr[idx];
					max_idx = idx;
				}
			}
			temp = arr[arr.length - 2];
			arr[arr.length - 2] = max;
			arr[max_idx] = temp;
			long sum = 0l;
			for (int idx = 0; idx < n + 1; idx++) {
				sum += arr[idx];
			}
			int i = -1;
			for (int idx = 0; idx < n + 1; idx++) {
				if (idx == n && (sum - arr[idx] == arr[idx] || sum - arr[idx] == arr[n + 1])) {
					i = idx;
					break;
				}
				if (sum - arr[idx] == arr[n + 1]) {
					i = idx;
					break;
				}
			}
			if (i == -1) {
				out.write(-1 + "");
				out.newLine();
				continue;
			}
			for (int idx = 0; idx < arr.length - 1; idx++) {
				if (idx == i)
					continue;
				out.write(arr[idx] + " ");
			}
			out.newLine();
		}
		out.close();
	}

	static 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());
		}

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

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

		public int[] readArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++)
				arr[i] = nextInt();
			return arr;
		}
	}

}