Out of Boundary - Walkthrough

Count paths that exit an $m \times n$ grid in exactly $k$ moves. Each move goes up/down/left/right. $dp[step][r][c]$ = number of paths at $(r, c)$ after $step$ moves. Transitions: each cell receives from 4 neighbors.

When a move goes out of bounds, it counts as an exit. Track exits at each step. Total exits = sum of paths that exit at each step from 1 to $k$. Take modulo as counts get large. Use modular arithmetic for counting paths. The mod operation distributes over addition correctly.