Find all positive integers $k$ such that for any positive integer $n$, $2^{(k-1)n+1}$ does not divide $\frac{(kn)!}{n!}$.

From [olympiad problem](http://www.artofproblemsolving.com/community/c6h1238141p6307368)

I'm curious So far no one to solve this problem,Maybe it is very difficult May be other reasons? But I really want to know how to solve this problem more easy?