Problem: We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.

<image>

A pyramid with N=4 steps

Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:

* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.



<image>

Writing integers into the blocks

Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.

Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.

Constraints

* 2≤N≤10^5
* 1≤x≤2N-1

Input

The input is given from Standard Input in the following format:


N x


Output

If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.

Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.

The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.

Examples

Input

4 4


Output

Yes
1
6
3
7
4
5
2


Input

2 1


Output

No

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.awt.geom.*;
import java.math.*;

public class Main {

	static final Scanner in = new Scanner(System.in);
	static final PrintWriter out = new PrintWriter(System.out,false);
	static boolean debug = false;

	static void solve() {
		int n = in.nextInt();
		int x = in.nextInt();


		if (n == 1) {
			if (x == 1) {
				out.println("Yes");
				out.println(1);
			} else {
				out.println("No");
			}

			return;
		}

		if (n == 2) {
			if (x == 2) {
				out.println("Yes");
				for (int i=1; i<=3; i++) {
					out.println(i);
				}
			} else {
				out.println("No");
			}

			return;
		}

		if (x == 1 || x == 2*n-1) {
			out.println("No");
		} else {
			out.println("Yes");

			ArrayList<Integer> ans = new ArrayList<>();

			if (x == 2) {
				ans.add(2*n-1);
				ans.add(1);
				ans.add(2);
				ans.add(2*n-2);

				int m = n;
				int p = 3;
				for (int i=0; i<m-3; i++) {
					ans.add(0, p);
					p++;
				}

				while (p != 2*n-2) {
					ans.add(p);
					p++;
				}

			} else if (x == 2*n-2) {
				ans.add(1);
				ans.add(2*n-2);
				ans.add(2*n-1);
				ans.add(2);

				int m = n;
				int p = 3;
				for (int i=0; i<m-2; i++) {
					ans.add(0, p);
					p++;
				}
				while (p != 2*n-1) {
					ans.add(p);
					p++;
				}

			} else {
				ans.add(1);
				ans.add(x);
				ans.add(2*n-1);
				ans.add(2);

				int m = n;
				int p = 3;
				if (p == x) p++;
				for (int i=0; i<m-2; i++) {
					ans.add(0, p);
					p++;
					if (p == x) p++;
				}
				while (p != 2*n-1) {
					ans.add(p);
					p++;
					if (p == x) p++;
				}
			}


			for (int i=0; i<2*n-1; i++) {
				out.println(ans.get(i));
			}
		}
	}

	public static void main(String[] args) {
		debug = args.length > 0;
		long start = System.nanoTime();

		solve();
		out.flush();

		long end = System.nanoTime();
		dump((end - start) / 1000000 + " ms");
		in.close();
		out.close();
	}

	static void dump(Object... o) { if (debug) System.err.println(Arrays.deepToString(o)); }
}