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.

Input

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

Output

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

Note

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