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. 
entry = input().split()

p = int(entry[0])
k = int(entry[1])

forward = 1
backward = k + 1

answer = []

for controller in range((k//2) + 1):

    answer.append(str(forward))
    if forward != backward:
        answer.append(str(backward))

    forward += 1
    backward -= 1

for filler in range(k+2, p+1):
    answer.append(str(filler))

print(' '.join(answer))
 				   	 			   	    		 			