CMO 2020 Problem 3

Let $S$ be a set, $|S|=35$ . A set $F$ of mappings from $S$ to itself is called to be satisfying property $P(k)$ , if for any $x,y\in S$ , there exist $f_1, \cdots, f_k \in F$ (not necessarily different), such that $f_k(f_{k-1}(\cdots (f_1(x))))=f_k(f_{k-1}(\cdots (f_1(y))))$ . Find the least positive integer $m$ , such that if $F$ satisfies property $P(2019)$ , then it also satisfies property $P(m)$ .