Leetcode 3665. Twisted Mirror Path Count

Count the number of unique paths from (0,0) to (m-1,n-1) on an m×n binary grid where moves are only right or down, but attempting to enter a mirror cell redirects the robot perpendicularly (right→down, down→right) and can chain until a non-mirror or out-of-bounds (which makes the path invalid). The core challenge is counting direction-aware transitions (with possible repeated reflections) efficiently and returning the total modulo 1e9+7.