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, raw_input().split())

odd = 1
even = n
a= [0]*n
kcount = 0
for i in range(k):

	if i%2 == 0:
		a[i] = even
		even -= 1
		
	else:
		a[i] = odd
		odd += 1

# print a

if k % 2 == 0:
	for j in range(k, n):
		a[j] = odd 
		odd += 1

else:
	for j in range(k, n):
		#print j
		a[j] = even
		even -= 1


print ' '.join(map(str, a))