Cat and Mouse II

Determine whether the mouse can force a win in an alternating perfect-information game on a grid with walls and food, where each turn the mouse or cat can jump up to their respective max distance (or stay), and the game ends if the cat catches the mouse, either reaches food first, or the mouse fails to reach food within 1000 turns. The core challenge is computing the winner under optimal play over the finite state space of (mouse_pos, cat_pos, turn) — i.e., a minimax/retrograde-analysis on the game graph with jump constraints and obstacles.