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.

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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.



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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:
/* Filename: AGC006B.java
 * Author: Mushiyo
 */

import java.util.Scanner;
import java.util.Arrays;

public class Main{

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);

		while (input.hasNext()) {
			int N = input.nextInt();
			int x = input.nextInt();
			int rowNLen = 2 * N - 1;

			if (x == 1 || x == rowNLen) {
				System.out.println("No");
			} else {
				int[] ans = new int[rowNLen + 1];
				for (int i = 0; i < ans.length; ++i) {
					ans[i] = i;
				}

				int mid = N;
				int tmp = ans[mid];
				ans[mid] = x;
				ans[x] = tmp;
				//System.out.println(Arrays.toString(ans));

				tmp = ans[mid - 1];
				ans[mid - 1] = rowNLen;
				ans[rowNLen] = tmp;
				//System.out.println(Arrays.toString(ans));

				if (ans[mid + 1] != 1) {
					tmp = ans[mid + 1];
					ans[mid + 1] = 1;
					ans[1] = tmp;
				}
				//System.out.println(Arrays.toString(ans));
				System.out.println("Yes");
				StringBuilder ansOut = new StringBuilder();
				for (int i = 1; i < ans.length; ++i) {
					ansOut.append(String.format("%d\n", ans[i]));
				}
				System.out.print(ansOut);
			}
		}
	}
}