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 CPP):

Solution:
#include <cstdio>

int main()
{
  int n,x;
  scanf("%d%d",&n,&x);
  if(x!=1&&x!=2*n-1){
    puts("Yes");
    int c=(x==2?5:x==3?5:1);
    int g=(x==2?-1:1);
    for(int i=0;i<2*n-1;i++){
      int k;
      if(i<n-2||n+1<i){
	k=c;
	c++;
	if(c==x-2){
	  c=x+2;
	}
      }
      else{
	k=(i==n-2?x-1*g:i==n-1?x:i==n?x+1*g:x-2*g);
      }
      printf("%d\n",k);
    }
  }
  else{
    puts("No");
  }
  return 0;
}