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. 
'''
Fuad Ashraful Mehmet 
University of Asia Pacific
Category:combinatorics +data structure
'''

import collections

n,k=map(int,input().split())
d= collections.deque()

for i in range(1,n+1):
  d.append(i)


res=[]
turn=0
while k>1:

  if turn==0:
    res.append(d.popleft())
  else:
    res.append(d.pop())
  turn=1-turn
  k-=1


if turn==1:

  while d:
    res.append(d.pop())
  
else:
  while d:
    res.append(d.popleft())


print(*res)




