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:
import sys
stdin = sys.stdin

def li(): return [int(x) for x in stdin.readline().split()]
def li_(): return [int(x)-1 for x in stdin.readline().split()]
def lf(): return [float(x) for x in stdin.readline().split()]
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(ns())
def nf(): return float(ns())

n,x = li()

if n == 2 and x == 2:
    print("Yes")
    for i in range(1,4):
        print(i)
        
elif (n == 2 and x == 1) or (n == 2 and x == 3):
    print("No")

elif x == 1 or x == 2*n-1:
    print("No")

elif x == 2:
    ans = [i for i in range(1,x-1)] + [i for i in range(x+3, 2*n)]
    ans = ans[:n-2] + [x+2, x, x-1, x+1] + ans[n-2:]
    
    print("Yes")
    for ai in ans:
        print(ai)
    
else:
    ans = [i for i in range(1,x-2)] + [i for i in range(x+2, 2*n)]
    ans = ans[:n-2] + [x-1, x, x+1, x-2] + ans[n-2:]
    
    print("Yes")
    for ai in ans:
        print(ai)