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. 
a = input().split()
for i in range(len(a)):
	a[i] = int(a[i])
n=a[0]
k=a[1]
j=0
q=n
w=n-k+1
for i in range(n-k):
	print(i+1)
for i in range(k):#n-k+1
	if not i%2:
		#chet
		print(q)
		q=q-1
	else:
		print(w)
		w=w+1

