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())
r = 1
ans = [1]
while r < k :
	ans += [abs(ans[-1]-(-1)**(r%2)*(n-r))]
	r+=1

if n/2. < ans[-1] : ans += range(ans[-1]-1,ans[-1]-(n-k)-1,-1)	
else : ans += range(ans[-1]+1,ans[-1]+(n-k)+1)
	
print ' '.join(map(str,ans))
	