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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int x = sc.nextInt();

        if (N==2) {
            if (x==2) {
                System.out.println("Yes");
                for (int i=1;i<=3;i++) {
                    System.out.println(i);
                }
            } else {
                System.out.println("No");
            }
            return;
        }
        // if (N==3) {
        //     if (x==2) {
        //         System.out.println("Yes");
        //         System.out.println(3);
        //         System.out.println(1);
        //         System.out.println(2);
        //         System.out.println(4);
        //         System.out.println(5);
        //     } else if (x==3) {
        //         System.out.println("Yes");
        //         for (int i=1;i<=5;i++) {
        //             System.out.println(i);
        //         }
        //     } else if (x==4) {
        //         System.out.println("Yes");
        //         System.out.println(3);
        //         System.out.println(4);
        //         System.out.println(5);
        //         System.out.println(1);
        //         System.out.println(2);
        //     } else {
        //         System.out.println("No");
        //     }
        //     return;
        // }
        if (2<=x && x<=2*N-1-1) {
            System.out.println("Yes");
            ArrayList<Integer> before = new ArrayList<Integer>();
            ArrayList<Integer> after = new ArrayList<Integer>();
            int cnt = 0;
            for (int i=1;i<=2*N-1;i++) {
                if (i==x-1 || i==x || i==x+1) continue;
                cnt++;
                if (cnt<=N-2) {
                    before.add(i);
                } else {
                    after.add(i);
                }
            }
            for (int i=0;i<N-2;i++) {
                System.out.println(before.get(i));
            }
            System.out.println(x-1);
            System.out.println(x);
            System.out.println(x+1);
            for (int i=0;i<N-2;i++) {
                System.out.println(after.get(i));
            }
        } else {
            System.out.println("No");
        }
    }
}