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())
Las = 2 * N - 1
NO = "No"
YES = "Yes"

if N == 2:
	if x == 2:
		print(YES)
		for i in range(1, 3+1):
			print(i)
	else:
		print(NO)
else:
	if x >= 3 and x <= Las - 2:
		print(YES)

		cnt = 1
		for i in range(1, N-2):
			if cnt == x - 2:
				cnt += 5
				print(cnt)
				cnt += 1
			else:
				print(cnt)
				cnt += 1
		print(x-2)
		print(x+1)
		print(x)
		print(x-1)
		print(x+2)
		for i in range(1, N-2):
			if cnt == x - 2:
				cnt += 5
				print(cnt)
				cnt += 1
			else:
				print(cnt)
				cnt += 1
	elif x == 2:
		print(YES)
		flag = True
		for i in range(1, Las + 1):
			if i == N - 1:
				print(1)
			elif i == N:
				print(2)
				flag = False
			elif flag:
				print(i + 2)
			else:
				print(i)
	elif x == Las - 1:
		print(YES)
		flag = True
		for i in range(1, Las + 1):
			if i == N - 1:
				print(Las)
			elif i == N:
				print(Las - 1)
				flag = False
			elif flag:
				print(i)
			else:
				print(i-2)
	else:
		print(NO)