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. 
import time
def process(n,k):
	ret=[]
	tmp=[]
	#for i in range(n-1):
		#tmp.append(i+2)
	"""ret.append(1)
	sign=1
	i=k
	curr=1"""
	start=1
	end=k+1
	while start<=end:
		ret.append(start)
		if start!=end:
			ret.append(end)
		start+=1
		end-=1
	if k<n-1:
		i=k+2
		while i<n+1:
			ret.append(i)
			i=i+1
	for i in range(len(ret)):
		print ret[i],
if __name__=="__main__":
	s=raw_input()
	nums=map(int,list(s.split(" ")))
	process(int(nums[0]),int(nums[1]))



