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 PYTHON3):

Solution:
n, x = map(int, input().split())
ans = [None]*(2*n-1)
if x == 2*n-1 or x == 1:
    print("No")

elif n == 2:
    print("Yes")
    for i in range(1, 4):
        print(i)
else:
    print("Yes")
    if x == 2*n-2:
        num = 1
        for i in range(n+1, 2*n-1):
            ans[i] = num
            num += 1
        for i in range(n+1):
            ans[i] = num
            num += 1

    else:
        ans[n-1] = x
        ans[n] = x-1
        ans[n+1] = x+2
        ans[n-2] = x+1
        num = 1
        for i in range(2*n-1):
            if x-1 <= num <= x+2:
                num = x+3
            if n-2 <= i <= n+1:
                continue
            ans[i] = num
            num += 1
    for i in range(2*n-1):
        print(ans[i])