ISL 2018 A4

Let $a_{0}, a_{1}, a_{2}, \ldots$ be a sequence of real numbers such that $a_{0}=0, a_{1}=1$, and for every $n \geqslant 2$ there exists $1 \leqslant k \leqslant n$ satisfying $$a_{n}=\frac{a_{n-1}+\cdots+a_{n-k}}{k}$$ Find the maximal possible value of $a_{2018}-a_{2017}$. (Belgium)