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. 
line = raw_input().strip()
n, k = int(line.split()[0]), int(line.split()[1])
i, j = n, 1

print i,
i -= 1
curr = False

while k > 1:
	if curr:
		print i,
		i -= 1
	else:
		print j,
		j += 1
	curr = not curr
	k -= 1

if curr:
	while j <= i:
		print j,
		j += 1
else:
	while i >= j:
		print i,
		i -= 1
