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 PYTHON):

Solution:
# -*- coding: utf-8 -*-
import sys,copy,math,heapq,itertools as it,fractions,re,bisect,collections as coll

def med(a):
    return sorted(a)[1]

def simu(a):
    while len(a) > 1:
        a = [med([a[i], a[i + 1], a[i + 2]]) for i in xrange(len(a) - 2)]
    return a[0]

#for ele in it.permutations(xrange(1, 8)):
#    if simu(ele) == 2:
#        print ele

N, x = map(int, raw_input().split())
d = x - N
if 1 < x <= 2*N - 2:
    print "Yes"
    ans = [(i + d)%(2*N - 1) + 1 for i in xrange(2*N - 1)]
    print "\n".join(map(str, ans))
    #print simu(ans)
else:
    print "No"