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:
n,x=map(int,input().split())
if n==2and x==2:
    print('Yes',*[1,2,3],sep='\n')
    exit()
a=[[]for _ in range(2*n-1)]
a[n-1]=x
f=[0]*2*n
f[x]=1
try:
    if x>2*n-3:
        a[n-3]=x-2
        a[n-2]=x+1
        a[n]=x-1
        f[x-2]=f[x-1]=f[x+1]=1
    else:
        a[n-3]=x+2
        a[n-2]=x-1
        a[n]=x+1
        f[x-1]=f[x+1]=f[x+2]=1
    if f[0]:
        1/0
except:
    print('No')
    exit()
i=0
for j,v in enumerate(f[1:],1):
    if v:continue
    while a[i]:i+=1
    a[i]=j
print('Yes',*a,sep='\n')