Školjka

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 $n\geq 2$ there exists $1\geq k \geq n$ satisfying $$a_n=\frac{a_{n-1}+\dots + a_{n-k}}{k}.$$Find the maximum possible value of $a_{2018}-a_{2017}$.