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. 
n, k = map(int, input().split())
cur1 = 1
cur2 = n
temp = 0
tt = 0
for i in range(n):
	if i < k:
		if (i & 1) == 0:
			print(cur1, end = ' ')
			cur1 += 1
			temp = cur1
			tt = 1
		else:
			print(cur2, end = ' ')
			cur2 -= 1
			temp = cur2
			tt = -1
	else:
		if tt == 1:
			print(cur1, end = ' ')
			cur1 += 1
		else:
			print(cur2, end = ' ')
			cur2 -= 1
print()
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