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>
#include <cstdlib>
#define repi(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,a) repi(i,0,a)

int N, x;
int p[200000];

int main()
{
  scanf( "%d%d", &N, &x );

  if( x == 1 || x == 2*N-1 )
  {
    puts( "No" );
   
    return 0;
  }

  puts( "Yes" );

  int mid = (2*N-1)/2;
  p[mid] = x;
  p[mid-1] = x-1;
  p[mid+1] = x+1;

  int ptr = 0;
  repi( i, 1, 2*N-1+1 ) if( abs(i-x) > 1 )
  {
    if( ptr == mid-1 )
      ptr += 3;

    p[ptr++] = i;
  }

  rep( i, 2*N-1 )
    printf( "%d\n", p[i] );

  return 0;
}