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. 
# Given N and K, print a permutation of N numbers s.t. 
# N - 1 differences between two consecutive terms has
# K distinct values.

# You can greedily construct the sequence by alternatively filling in 
# K numbers from either ends of [1, 2, ..., N-1, N]. 
# e.g. N = 5, K = 3
# 1 5 2 3 4

def solve(n, k):
	
	l = 1
	r = n
	ans = []
	if k == 1:
		return ' '.join(map(str, range(1, n+1)))
	num = 0
	while k > 0:
		if num % 2 == 0:
			ans.append(l)
			l += 1
		else:
			ans.append(r)
			r -= 1
		num += 1
		k -= 1

	num_copy = num
	while num < n:
		if num_copy % 2 == 0:
			ans.append(r)
			r -= 1
			num += 1
		else:
			ans.append(l)
			l += 1
			num += 1

	return ' '.join(map(str, ans))

# print solve(3, 2)
# print solve(3, 1)
# print solve(5, 2)
n, k = map(int, raw_input().split())
print solve(n, k)