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) = list(map(int,input().split()))
counter = n - k
diverse = True

i = 1
nums = []
while i <= counter:
    nums.append(i)
    i += 1

i = k
while i >= 1:
    if diverse:
        nums.append(counter + i)
        counter += i
        diverse = False
    else:
        nums.append(counter - i)
        counter -= i
        diverse = True
    i -= 1
print(*nums)
   		 	   		  	 		 			 		 	 	