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 x==1 or x==2*N-1:
    print("No")
elif N==2:
    print("Yes")
    for i in range(1,4):
        print(i)
else:
    lst=[0 for i in range(2*N-1)]
    nlst=set([i for i in range(1,2*N)])
    if x>=N:
        lst[N-1]=x
        lst[N]=x+1
        lst[N+1]=x-1
        lst[N-2]=x-2
        nlst.remove(x)
        nlst.remove(x+1)
        nlst.remove(x-1)
        nlst.remove(x-2)
    else:
        lst[N-1]=x
        lst[N]=x-1
        lst[N+1]=x+1
        lst[N-2]=x+2
        nlst.remove(x)
        nlst.remove(x-1)
        nlst.remove(x+1)
        nlst.remove(x+2)

    idxlst=set([i for i in range(2*N-1)])
    idxlst.remove(N-2)
    idxlst.remove(N-1)
    idxlst.remove(N)
    idxlst.remove(N+1)

    nlst=list(nlst)
    idxlst=list(idxlst)
    for n,i in zip(nlst,idxlst):
        lst[i]=n
    print("Yes")
    for i in lst:
        print(i)