2004 AIME I 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 \left \lfloor{z}\right \rfloor denotes the greatest integer that is less than or equal to z.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.