Recurrence Reachability

Given two integers $x$ and $y$, where $x \lt y$, we define a function $f_{x, y}$ with the following rules: - $f_{x, y}(0) = x$ - $f_{x, y}(1) = y$ - For every integer $k \ge 2$, $$ f_{x, y}(k) = 3\cdot f_{x, y}(k-1) - 2\cdot f_{x, y}(k-2) $$ You're given two integers $N$ and $M$. Your task is to find any pair of integers $(x, y)$ such that: - $1 \le x \lt y \le N$, and - There exists some integ