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Description

You are given two numbers $n$ and $k$.

You are required to construct a permutation $p_1, p_2, ..., p_n$ of numbers $1, 2, ..., n$ such that there are exactly $k$ different numbers in $|p_1 - p_2|$, $|p_2 - p_3|$, ..., $|p_{n-1} - p_n|$.

Input

Only one line contains two integers $n$ and $k$.

$1 \leq k < n \leq 100000$.

Output

Print $n$ integers forming the permutation.

If there are multiple answers, print any of them.

If there are no such permutation, print -1.

Samples

3 1

1 2 3

Resources

The 15th UESTC Programming Contest Preliminary