Beauty of Segments

You are given $N$ segments $(l_1, r_1), (l_2, r_2), (l_N, r_N)$ and two integers $A$ and $B$. Let's define *playing a game* with two parameters $(x, y)$, where $0 \le x \le N$, as the following recursive process: - If $x = 0$, the game ends immediately. - Otherwise, if $y \le l_x$ or $r_x \le y$, end this game and play a game with $(x-1, y)$. - Otherwise (if $l_x \lt y \lt r_x$), you must choose o