#P482A. Diverse Permutation

    ID: 3111 Type: RemoteJudge 1000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>constructive algorithmsgreedy*1200

Diverse Permutation

No submission language available for this problem.

Description

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.

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Print n integers forming the permutation. If there are multiple answers, print any of them.

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.

Samples

3 2

1 3 2

3 1

1 2 3

5 2

1 3 2 4 5

Note

By |x| we denote the absolute value of number x.