Reflections of Rays in a Mirror

From the point (-1, -1), two rays are sent making angles of $45^{\circ}$ with the line $x+y=0$. These rays get reflected from the mirror $x+2y=1$. If the equations of the reflected rays are $ax+by=9$ and $cx+dy=7, a, b, c, d \in \mathbb{Z}$, then the value of $ad+bc$ is _____.