Diverse Permutation

题意翻译

题面： 构造一个n的排列,使将排列相邻两数相减取绝对值所得到的序列中刚好有k种值. 输入格式： 一行仅一个n,k. 输出格式： 一个n的排列,如有多组答案,输出任意一组. 数据范围： n:[1,1e5] k:[1,n) 注意： 本题有SPJ. 翻译贡献者：尘染梦

题目描述

Permutation $ p $ is an ordered set of integers $ p_{1},p_{2},...,p_{n} $ , consisting of $ n $ distinct positive integers not larger than $ n $ . We'll denote as $ n $ the length of permutation $ p_{1},p_{2},...,p_{n} $ . Your task is to find such permutation $ p $ of length $ n $ , that the group of numbers $ |p_{1}-p_{2}|,|p_{2}-p_{3}|,...,|p_{n-1}-p_{n}| $ has exactly $ k $ distinct elements.

输入输出格式

输入格式

The single line of the input contains two space-separated positive integers $ n $ , $ k $ ( $ 1<=k<n<=10^{5} $ ).

输出格式

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

输入输出样例

输入样例 #1

3 2

输出样例 #1

1 3 2

输入样例 #2

3 1

输出样例 #2

1 2 3

输入样例 #3

5 2

输出样例 #3

1 3 2 4 5

说明

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