Product Path

You are given two integers $N$ and $M$. Consider two infinite arrays $A$ and $B$, where - $A_i = \max\left(i, \frac{N}{i}\right)$ if $i$ divides $N$; and $A_i = 0$ otherwise. - $B_i = \max\left(i, \frac{M}{i}\right)$ if $i$ divides $M$; and $B_i = 0$ otherwise. For example, if $N = 6$, then $A = [6, 3, 3, 0, 0, 6, 0, 0, 0, \ldots]$ You are standing on the 2D plane, at point $(1, 1)$. In one m