In a rectangular coordinate plane, point $A(a, b)$; its reflection with respect to point $B(3, 0)$ is point $C$, and its reflection with respect to the $y$-axis is point $D$.
Given that the equation of the line passing through points $C$ and $D$ is $y = -x - 1$, what is the sum $a + b$?
A) 7
B) 13
C) 15
D) 19
E) 24