Diverse Permutation
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.