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:
# x が1 か 2N - 1の場合、中央値としてこれらが上がってくることはないため"No"
# それ以外の場合、
# x = Nの場合、順列そのまま1,2,3...2N-1でOK
# x < Nの場合、xを真ん中に置き、その左に1を置く。
# あとは左から順に1,2,3...と埋めていけばOK
# x > Nの場合、xを真ん中に置き、その右に2N - 1を置く。
# あとは左から順に1,2,3...と埋めていけばOK

import sys
readline = sys.stdin.readline

N,x = map(int,readline().split())

if x == 1 or x == 2 * N - 1:
  print("No")
  exit(0)
elif x == N:
  A = [i + 1 for i in range(2 * N - 1)]
elif x < N:
  A = [0 for i in range(2 * N - 1)]
  A[N - 1] = x
  A[N - 2] = 1
  ind = 0
  for num in range(2,2 * N):
    if num in (1,x):
      continue
    if A[ind] != 0:
      ind += 2
    A[ind] = num
    ind += 1
elif x > N:
  A = [0 for i in range(2 * N - 1)]
  A[N - 1] = x
  A[N] = 2 * N - 1
  ind = 0
  for num in range(1,2 * N):
    if num in (x,2 * N - 1):
      continue
    if A[ind] != 0:
      ind += 2
    A[ind] = num
    ind += 1

print("Yes")
for a in A:
  print(a)