AIME 2004a Problem 12

Let $S$ be the set of ordered pairs $(x, y)$ such that $0 < x \le 1, 0<y\le 1,$ and $\left\lfloor\log_2{\left(\frac 1x\right)}\right\rfloor$ and $\left\lfloor\log_5{\left(\frac 1y\right)}\right\rfloor$ are both even. Given that the area of the graph of $S$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$ The notation $\lfloor{z}\rfloor$ denotes the greatest integer that is less than or equal to $z.$