Coming up with a condition for index selection from a set for a specific problem

Question

In my research I have come across the following problem. I have two sets of real numbers, say $\{a_i\},\ \{b_i\},\ i=1,2,\cdots,\ n$. Let $S$ be a given set such that $S\subset \{1,2,\cdots,\ n\}$. Now, I am choosing $m$ indices among $1,2,\cdots,\ n$ such that they correspond to the $m$ largest absolute values $|a_{\pi(i)}|,\ i=1,2,\cdots,\ m$. I need to come up with a condition on $a,b,S$ such that $$\arg\max_{i\in \{\pi(1),\pi(2),\cdots,\ \pi(m)\}} |b_i|\in S$$ I do not find any literature that talks about such a situation. Please help.