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. 
import math

n, k = map(int, raw_input().split())

nums = range(1, n + 1)
left = 0
right = len(nums) - 1
left_start = True
print nums[left],
left += 1
left_start = False
while k != 1:
  if left_start:
    print nums[left],
    left += 1
    left_start = False
  else:
    print nums[right],
    right -= 1
    left_start = True
  k -= 1
if not left_start:
  while left <= right:
    print nums[left],
    left += 1

else:
  while right >= left:
    print nums[right],
    right -= 1
