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:
def b_median_pyramid_easy(N, X):
    # 頂点の列とその右の列が常にXになるような数列を構成できればいい
    if X in [1, 2 * N - 1]:
        return 'No'  # この2つは中央値になりえないので、構成不可能
    if N == 2:
        return 'Yes\n1\n2\n3'
        # 下の処理はN>=3のときに行う。N=2, X=2のときは 1 2 3 が解になる

    ans_seq = [k for k in range(1, 2 * N)]
    if X == 2:
        # 1から2*N-1までの数字を昇順に並べ、値がXの周辺の数字を4つ取り出し、
        # 中央に入れる
        tmp = [k for k in range(1, X - 1)] + [k for k in range(X + 3, 2 * N)]
        center = [X + 1, X, X - 1, X + 2]
    else:
        tmp = [k for k in range(1, X - 2)] + [k for k in range(X + 2, 2 * N)]
        center = [X - 1, X, X + 1, X - 2]
    ans_seq = tmp[:N - 2] + center + tmp[N - 2:]
    ans = 'Yes\n' + '\n'.join(map(str, ans_seq))
    return ans

N, X = [int(i) for i in input().split()]
print(b_median_pyramid_easy(N, X))