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

def Next(m, n):
  return n + 1 - m if m * 2 < n else n + 2 - m 

x = 1

for i in xrange(k):
  print x,
  if i != k - 1: x = Next(x, n)

dir = 1 if x * 2 <= n else -1

for i in xrange(n - k):
  x += dir
  print x,
