Coordinate Geometry: JEE Main 2026 Mathematics question

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 ______.