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.util.*;
import java.io.*;
public class Prob16 {
	public static void main(String[] args) throws IOException {
		Reader sc = new Reader();
		PrintWriter out = new PrintWriter(System.out);
		int t = sc.nextInt();
		for(int i = 0; i < t; i++) {
			int n = sc.nextInt(), x = sc.nextInt();
			int[] a = new int[n];
			for(int j = 0; j < n; j++) a[j] = sc.nextInt();
			Arrays.sort(a);
			int sum = 0;
			boolean works = true;
			for(int j = 0; j < n; j++) {
				sum += a[j];
				if(sum == x  && j == n - 1) works = false;
				else if(sum == x) swap(a, j, j + 1);
			}
			if(works) {
				out.println("YES");
				for(int j : a) out.print(j + " ");
				out.println();
			}else out.println("NO");
			 
		}
		out.close();
		
	}
	

	private static void swap(int[] a, int i, int j) {
		int foo = a[i];
		a[i] = a[j];
		a[j] = foo;
	}


		static class Reader {
			final private int BUFFER_SIZE = 1 << 16;
			private DataInputStream din;
			private byte[] buffer;
			private int bufferPointer, bytesRead;

			public Reader()
			{
				din = new DataInputStream(System.in);
				buffer = new byte[BUFFER_SIZE];
				bufferPointer = bytesRead = 0;
			}

			public Reader(String file_name) throws IOException
			{
				din = new DataInputStream(
					new FileInputStream(file_name));
				buffer = new byte[BUFFER_SIZE];
				bufferPointer = bytesRead = 0;
			}

			public String readLine() throws IOException
			{
				byte[] buf = new byte[64]; // line length
				int cnt = 0, c;
				while ((c = read()) != -1) {
					if (c == '\n') {
						if (cnt != 0) {
							break;
						}
						else {
							continue;
						}
					}
					buf[cnt++] = (byte)c;
				}
				return new String(buf, 0, cnt);
			}

			public int nextInt() throws IOException
			{
				int ret = 0;
				byte c = read();
				while (c <= ' ') {
					c = read();
				}
				boolean neg = (c == '-');
				if (neg)
					c = read();
				do {
					ret = ret * 10 + c - '0';
				} while ((c = read()) >= '0' && c <= '9');

				if (neg)
					return -ret;
				return ret;
			}

			public long nextLong() throws IOException
			{
				long ret = 0;
				byte c = read();
				while (c <= ' ')
					c = read();
				boolean neg = (c == '-');
				if (neg)
					c = read();
				do {
					ret = ret * 10 + c - '0';
				} while ((c = read()) >= '0' && c <= '9');
				if (neg)
					return -ret;
				return ret;
			}

			public double nextDouble() throws IOException
			{
				double ret = 0, div = 1;
				byte c = read();
				while (c <= ' ')
					c = read();
				boolean neg = (c == '-');
				if (neg)
					c = read();

				do {
					ret = ret * 10 + c - '0';
				} while ((c = read()) >= '0' && c <= '9');

				if (c == '.') {
					while ((c = read()) >= '0' && c <= '9') {
						ret += (c - '0') / (div *= 10);
					}
				}

				if (neg)
					return -ret;
				return ret;
			}

			private void fillBuffer() throws IOException
			{
				bytesRead = din.read(buffer, bufferPointer = 0,
									BUFFER_SIZE);
				if (bytesRead == -1)
					buffer[0] = -1;
			}

			private byte read() throws IOException
			{
				if (bufferPointer == bytesRead)
					fillBuffer();
				return buffer[bufferPointer++];
			}

			public void close() throws IOException
			{
				if (din == null)
					return;
				din.close();
			}
		}
}