Diverse Permutation

1000ms

262144K

Description:

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.

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:

3 2

Sample Output:

1 3 2

Sample Input:

3 1

Sample Output:

1 2 3

Sample Input:

5 2

Sample Output:

1 3 2 4 5

Note:

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

Informação

Provedor Codeforces

Código CF482A