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:

import java.util.Scanner;

public class Main {
    //       6
    //     2 6 5
    //   2 2 6 6 5
    // 3 2 1 7 6 5 4

    //       6
    //     6 6 2
    //   5 6 6 2 2
    // 3 5 6 7 1 2 4

    //       2
    //     6 2 2
    //   6 6 2 2 3
    // 5 6 7 1 2 3 4

    //     2
    //   2 2 4
    // 3 2 1 4 5

    //         8
    //       8 8 3
    //     6 8 8 2 2
    //   6 6 8 8 2 2 3
    // 7 4 6 9 8 1 2 5 3

    void run() {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt() * 2 - 1, x = sc.nextInt();
        if (x == 1 || x == n) {
            System.out.println("No");
            return;
        }
        System.out.println("Yes");
        int[] ans = new int[n];
        ans[n / 2] = x;
        ans[n / 2 - 1] = x + 1;
        ans[n / 2 + 1] = x - 1;

        int idx = 1;
        for (int i = 0; i < n; i++) {
            if (idx == x - 1) {
                idx += 3;
            }
            if (i == n / 2 - 1) {
                i += 2;
                continue;
            }
            ans[i] = idx++;
        }

        for (int i = 0; i < n; i++) {
            System.out.println(ans[i]);
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }
}