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>
using namespace std;
const int MAX = 300000 + 10;

int ans[MAX];

int main(){
  int n, x;
  scanf("%d %d", &n, &x);
  if (x == 1 || x == 2*n-1) {
    puts("No");
  } else {
    ans[n-1] = x;
    int now = n-2;
    for(int i = 1 ; i <= 2*n-1 ; i++) {
      if(i == x) continue;
      ans[now] = i;
      now--;
      if(now < 0) now = 2*n-2;
    }
    puts("Yes");
    for(int i = 0 ; i < 2 * n - 1 ; i++)
      printf("%d\n", ans[i]);
  }
  return 0;
}