Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Output

Print n integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2


Output

1 3 2


Input

3 1


Output

1 2 3


Input

5 2


Output

1 3 2 4 5

Note

By |x| we denote the absolute value of number x. 
from sys import exit
n,k = map(int,input().split())

if n<=2:
	print(*[i for i in range(1,n+1)])
	exit()
else:
	d = [1]
	for i in range(n+1):
		if k<=0:
			break
		if i%2==0:
			d.append(k+d[-1])
			k-=1
		else:
			d.append(d[-1]-k)
			k-=1
	if len(d)==n:
		print(*d)
	else:
		r = set(d)
		print(*d,*[i for i in range(1,n+1) if i not in r])

