Let k=2^6 \cdot 3^5 \cdot 5^2 \cdot 7^3 \cdot 53. Let S be the sum of \frac{\operatorname{gcd}(m, n)}{\operatorname{lcm}(m, n)} over all ordered pairs of positive integers (m, n) where m n=k. If S can be written in simplest form as \frac{r}{s}, compute r+s.