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:
import sys

N, x = map(int, input().split())
if x == 1 or x == 2 * N - 1:
    print("No")
    sys.exit()
if N == 2:
    print("Yes")
    print(1)
    print(2)
    print(3)
    sys.exit()

print("Yes")
n = 2 * N - 1
ans = [None] * n
tmp = ans[n//2-1:n//2+3]
# print(tmp)
if x != 2 * N - 2:
    tmp[0] = x + 1
    tmp[1] = x
    tmp[2] = x - 1
    tmp[3] = x + 2
else:
    tmp[0] = x - 1
    tmp[1] = x
    tmp[2] = x + 1
    tmp[3] = x - 2
cnt = 1

ans[n//2-1:n//2+3] = tmp
for i in range(n):
    if x != 2 *  N - 2:
        if cnt == x-1:
            cnt += 4
    else:
        if cnt == x-2:
            cnt += 4
    if ans[i] is None:
        ans[i] = cnt
        cnt += 1

for i in ans:
    print(i)