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.*;

/*
   AtCoder contest code
   coder : yoichidon
 */

public class Main {
    public static int[] solve(int N, int x){
        int[] ans = new int[2*N-1];
        if(N==2){
            return new int[]{1,2,3};
        }

        if(x==2){
            ans[N-2] = 2*N-1;
            ans[N-1] = 2;
            ans[N]   = 1;
            ans[N+1] = 2*N-2;
            int elm = 3;
            for(int index=0; index<2*N-1; index++){
                if(ans[index]==0){
                    ans[index]=elm;
                    elm++;
                }
            }
        }else{
            ans[N-2] = 1;
            ans[N-1] = x;
            ans[N]   = 2*N-1;
            ans[N+1] = 2;
            int elm = 3;
            for(int index=0; index<2*N-1; index++){
                if(elm==x) elm++;
                if(ans[index]==0){
                    ans[index]=elm;
                    elm++;
                }
            }
        }
        return ans;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int x = sc.nextInt();

        if(x==1 ||  x==2*N-1){
            System.out.println("No");
            return;
        }
        else{
            System.out.println("Yes");
        }
        int[] ans = solve(N,x);
        for(int i=0; i<ans.length; i++) System.out.println(ans[i]);


    }
}