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(x==1||x==2*n-1){
      System.out.println("No");
      return;
    }
    System.out.println("Yes");
    int[] cen = {x-2,x+1,x,x-1};
    int min = x-2;
    if(x==2){
      cen[0]=x+2;
      cen[1]=x-1;
      cen[3]=x+1;
      min=x-1;
    }
    if(n==2){
      System.out.println("1");
      System.out.println("2");
      System.out.println("3");
      return;
    }
    int num = 0;
    for(int i=0;i<n-3;i++){
      num++;
      if(num==min)num+=4;
      System.out.println(num);
    }
    for(int i=0;i<4;i++)System.out.println(cen[i]);
    for(int i=0;i<n-2;i++){
      num++;
      if(num==min)num+=4;
      System.out.println(num);
    }
  }
}