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())

if N == 2:
    if x == 2:
        print("Yes")
        print(1)
        print(2)
        print(3)
    else:
        print("No")

else:
    from collections import deque
    used = [True] + [False] * (2 * N)
    if x == 1 or x == 2*N-1:
        print("No")
        exit()
    elif x == 2:
        ans = deque([3, 1, 2, 4, 5])
        for i in range(1, 6):
            used[i] = True
    elif x == 3:
        ans = deque([4, 1, 3, 5, 2])
        for i in range(1, 6):
            used[i] = True
    else:
        ans = deque([x-3, x-1, x, x+1, x-2])
        for i in range(-3, 2):
            used[x+i] = True

    p = 0
    for i in range(2*N):
        if not used[i]:
            p^=1
            if p:
                ans.append(i)
            else:
                ans.appendleft(i)

    print("Yes")
    for e in list(ans):
        print(e)