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. 
s=raw_input().split()
n=int(s[0])
k=int(s[1])
h=n
l=2
if k==1:
	for i in range(1,n+1):
		print i,
	print ""

else:
	flag=1
	print 1,
	while(k!=1):
		if(flag==1):
			print h,
			h-=1
			flag=0
		else:
			print l,
			l+=1
			flag=1
		k-=1
	if(flag==1):
		while(l<=h):
			print l,
			l+=1
		print ""
		
	else:
		while(h>=l):
			print h,
			h-=1
		print ""
		