Permutation p is an ordered set of integers p₁,   p₂,   ...,   p_n, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p₁,   p₂,   ...,   p_n.

Your task is to find such permutation p of length n, that the group of numbers |p₁ - p₂|, |p₂ - p₃|, ..., |p_n - 1 - p_n| 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.