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