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())


def calc(a):
    b = []
    for i in range(len(a)-2):
        b.append(list(sorted(a[i:i+3]))[1])
    if len(b) == 1:
        return b[0]
    else:
        return calc(b)
"""
n = 5
max_ = []
for i in range(n):
    max_.append(i*2+1)

for i in range(n-1, 0, -1):
    max_.append(i*2)

print(calc(max_))
"""

if x == 1 or x == 2*n-1:
    print("No")
    exit()
print("Yes")

if x == 2:
    center = 2
    r1 = 1
    r2 = 3
    l = 4
else:
    center = x
    r1 = x+1
    r2 = 1
    l = 2

ans = []
y = 1
for i in range(n-2):
    while y in [center, r1, r2, l]:
        y+= 1
    ans.append(y)
    y+=1
ans.append(l)
ans.append(center)
ans.append(r1)
ans.append(r2)
for i in range(n-3):
    while y in [center, r1, r2, l]:
        y+=1
    ans.append(y)
    y+=1
if n == 2:
    ans = [1,2,3]
for x in ans:
    print(x)