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. 
arr = [int(x) for x in input().split()]
n = arr[0]
k = arr[1]
c = n - k
flag = True
resp = []

for i in range(1, n - k + 1):
  resp.append(str(i))

for i in range(k, 0, -1):
  if flag:
    c += i
    resp.append(str(c))
    flag = False
  else:
    c -= i
    resp.append(str(c))
    flag = True

resp = ' '.join(resp)
print (resp)

 	 					  			 	 	  		 		