Second Round

Given is the sequence of numbers $a_0,a_1,a_2,\dots ,a_{2020}$ with $a_0=0$. Furthermore, the following holds for every $k=1,2,\dots ,2020$: $$a_k=\{\begin{array}{ll}{a}_{k-1}\cdot k& \text{if }k\text{ is divisible by }8,\\ a_{k-1}+k& \text{if }k\text{ is not divisible by }8.\end{array}$$ What are the last two digits of $a_{2020}$?