69th Belarusian Mathematical Olympiad

Let $a_0,a_1,a_2,\dots$ be a sequence of real numbers such that $a_0=0$, $a_1=1$, and for every $n\ge 2$ there exists $1\le k\le n$ satisfying $$a_n=\frac{a_{n-1}+\cdots +a_{n-k}}{k}.$$ Find the maximal possible $a_{2018}-a_{2017}$.