Let $7\overbrace{5\cdots5}^{r}7$ denote the $(r+2)$ digit number where the first and the last digit are $7$ and the remaining $r$ digits are $5$. Consider the sum $S = 77 + 757 + 7557 + --- + 7\overbrace{5\cdots5}^{98}7$. If $S = \frac{7\overbrace{5\cdots5}^{99}7 + m}{n}$, where $m$ and $n$ are natural numbers less than $3000$, then the value of $m + n$ is _____.
