Problem: Phoenix has collected n pieces of gold, and he wants to weigh them together so he can feel rich. The i-th piece of gold has weight w_i. All weights are distinct. He will put his n pieces of gold on a weight scale, one piece at a time. 

The scale has an unusual defect: if the total weight on it is exactly x, it will explode. Can he put all n gold pieces onto the scale in some order, without the scale exploding during the process? If so, help him find some possible order. 

Formally, rearrange the array w so that for each i (1 ≤ i ≤ n), ∑_{j = 1}^{i}w_j ≠ x.

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains two integers n and x (1 ≤ n ≤ 100; 1 ≤ x ≤ 10^4) — the number of gold pieces that Phoenix has and the weight to avoid, respectively. 

The second line of each test case contains n space-separated integers (1 ≤ w_i ≤ 100) — the weights of the gold pieces. It is guaranteed that the weights are pairwise distinct.

Output

For each test case, if Phoenix cannot place all n pieces without the scale exploding, print NO. Otherwise, print YES followed by the rearranged array w. If there are multiple solutions, print any.

Example

Input


3
3 2
3 2 1
5 3
1 2 3 4 8
1 5
5


Output


YES
3 2 1
YES
8 1 2 3 4
NO

Note

In the first test case, Phoenix puts the gold piece with weight 3 on the scale first, then the piece with weight 2, and finally the piece with weight 1. The total weight on the scale is 3, then 5, then 6. The scale does not explode because the total weight on the scale is never 2.

In the second test case, the total weight on the scale is 8, 9, 11, 14, then 18. It is never 3.

In the third test case, Phoenix must put the gold piece with weight 5 on the scale, and the scale will always explode.

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(), x = in.nextInt();
			int sum = 0;
			int ind = -1;
			int[] a = new int[n];
			for(int i = 0; i < n; i++) {
				a[i] = in.nextInt();
				sum += a[i];
				if(sum == x) {
					ind = i;
				}
			}
			if(sum == x) {
				System.out.println("NO");
			}else {
				System.out.println("YES");
				for(int i = 0; i < n; i++) {
					if(i == ind) {
						System.out.print(a[ind+1] + " " + a[ind] + " ");
						i++;
					}else {
						System.out.print(a[i] + " ");
					}
				}
				System.out.println();
			}
		}
	}

	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;
	}

}