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 PYTHON3):

Solution:
import sys
from collections import deque
N,X=map(int,input().split())
if X==1 or X==2*N-1:
    print('No')
    sys.exit()
l=2*N-1
print('Yes')
if N==2:
    print(3)
    print(2)
    print(1)
    sys.exit()
if X==2:
    h=deque()
    h.append(3)
    h.append(2)
    h.append(1)
    h.append(4)
    s=0
    t=0
    while s!=N-2:
        t+=1
        if 4<t:
            s+=1
            h.appendleft(t)
    s=0
    while s!=N-3:
        t+=1
        if 4<t:
            s+=1
            h.append(t)
    print('\n'.join(map(str,h)))
    sys.exit()
    
h=deque()
h.append(X-1)
h.append(X)
h.append(X+1)
h.append(X-2)
s=0
t=0
while s!=N-2:
    t+=1
    if X+1<t or t<X-2:
        s+=1
        h.appendleft(t)
s=0
while s!=N-3:
    t+=1
    if X+1<t or t<X-2:
        s+=1
        h.append(t)
print('\n'.join(map(str,h)))