BG-MO 2020 Problem 6

Let $f(x)$ be a nonconstant real polynomial. The sequence $\{a_i\}_{i=1}^{\infty}$ of real numbers is strictly increasing and unbounded, as $$a_{i+1}<a_i+2020.$$ The integers $\lfloor{|f(a_1)|}\rfloor$ , $\lfloor{|f(a_2)|}\rfloor$ , $\lfloor{|f(a_3)|}\rfloor$ , $\dots$ are written consecutively in such a way that their digits form an infinite sequence of digits $\{s_k\}_{k=1}^{\infty}$ (here $s_k\in\{0, 1, \dots, 9\}$ ). $$ If $n\in\mathbb{N}$ , prove that among the numbers $\overline{s_{n(k-1)+1}s_{n(k-1)+2}\cdots s_{nk}}$ , where $k\in\mathbb{N}$ , all $n$ -digit numbers appear.