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. 
# python3
n, k = [int(x) for x in input().split()]

begin = 1
if k == 1:
	for x in range(1, n+1):
		print(x, end=" ")
else:
	# k = 2, +2 -1: 1 3 2
	# k = 3, +3 -2 + 1: 1 4 2 3 
	# k = 4, +4 -3 + 2 -1: 1 5 2 4 3 
	for y in range(n-k-1):
		print(begin+y, end=" ")
	diff = n-k
	high = n
	while high >= diff + 1:
		print(diff, end=" ")
		print(high, end=" ")
		diff += 1
		if diff == high:
			break
		high -= 1
	if diff == high and k % 2 != 1:
		print(high)


	# for z in range((k+1)/2):
	# 	# Difference continues to decrease by 1
	# 	print(diff + z, end=" ") 
	# 	print(n - z, end=" ")
	# if k % 2 == 0:
	# 	print((diff+n)//2)