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 D {
	
	public static void shuffleArray(long[] array) {
		int index;
		long temp;
		Random random = new Random();
		for (int i = array.length - 1; i > 0; i--) {
			index = random.nextInt(i + 1);
			temp = array[index];
			array[index] = array[i];
			array[i] = temp;
		}
	}
	
	public static void main(String[] args) throws FileNotFoundException {
		FastScanner fs = new FastScanner();
		FastOutput fo = new FastOutput();
		long initial_time = System.currentTimeMillis();
		int testcases = fs.nextInt();
		for (int tt = 0; tt < testcases; tt++) {
			//main code
			int n=fs.nextInt();
			long b[]=new long[n+2];
			for(int i=0;i<n+2;i++) {
				b[i]=fs.nextInt();
			}
			shuffleArray(b);
			Arrays.sort(b);
			if(n==1) {
				if(b[0]==b[1]) {
					fo.println(b[0]+"");
					continue;
				}
				else if(b[1]==b[2]) {
					fo.println(b[1]+"");
					continue;
				}
				else {
					fo.println(-1);
					continue;
				}
			}
			long sum=b[n];
			long cnt=0;
			for(int i=0;i<n;i++) {
				cnt+=b[i];
			}
			if(cnt==sum) {
				for(int i=0;i<n;i++) {
					fo.print(b[i]+" ");
				}
				fo.println("");
			}
			else {
				long sum2=b[n+1];
				long cnt2=0;
				for(int i=0;i<n+1;i++) {
					cnt2+=b[i];
				}
				long remove=cnt2-sum2;
				boolean is=false;
				for(int i=0;i<n+1;i++) {
					if(b[i]==remove) {
						is=true;
						break;
					}
				}
				if(is) {
					boolean is_removed=false;
					for(int i=0;i<n+1;i++) {
						if(b[i]==remove && !is_removed) {
							is_removed=true;
						}
						else {
							fo.print(b[i]+" ");
						}
					}
					fo.println("");
				}
				else {
					fo.println(-1);
				}
			}
		}
		fo.time(initial_time);
	}

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() throws FileNotFoundException {
			if (System.getProperty("ONLINE_JUDGE") == null) {
				//Read from the File...
				File file = new File("src\\input");
				br = new BufferedReader(new FileReader(file));
			} else {
				//Read from the System...
				br = new BufferedReader(new InputStreamReader(System.in));
			}
			st = new StringTokenizer("");
		}

		String next() {
			while (!st.hasMoreTokens())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

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

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

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

	static class FastOutput {
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

		void print(String str) {
			try {
				bw.write(str);
				bw.flush();
			} catch (IOException e) {
			}
		}

		void print(int num) {
			try {
				bw.write((num + ""));
				bw.flush();
			} catch (IOException e) {
			}
		}

		void println(String str) {
			try {
				bw.write(str + '\n');
				bw.flush();
			} catch (IOException e) {
			}
		}

		void println(int num) {
			try {
				bw.write(num + "" + '\n');
				bw.flush();
			} catch (IOException e) {
			}
		}

		void time(long init) {
			if (System.getProperty("ONLINE_JUDGE") == null) {
				System.out.println(System.currentTimeMillis() - init + "ms");
			}
		}
	}
}