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. 
from __future__ import print_function
s = input().split()
n = int(s[0])
k = int(s[1])
a = 1
b = k + 1
i = 0
while a < b:
    print(a, end = ' ')
    a += 1
    print(b, end = ' ')
    b -= 1
if a == b:
    print(a, end = ' ')
i = 2 + k
while i <= n:
    print(i, end = ' ')
    i += 1
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