Diverse Permutation

Time Limit: 1 second

Memory Limit: 256 megabytes

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.

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.

Sample Input

Input
3 2
Output
1 3 2
Input
3 1
Output
1 2 3
Input
5 2
Output
1 3 2 4 5

Sample Output

None

Hint

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

Source

None

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