A9765. Diverse Permutation

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.

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

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

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