Given a series of robots defined with initial position and velocity on a 101x103 toroidal grid, calculate where the robots will be after 100 iterations. Return the product of the number of robots in each quadrant of the final grid, ignoring the middle lines (since they’re odd).

Given Button A (ax, ay), Button B (bx, by), and Prize (px, py); how many times must you press Button A (a) and Button B (b) to reach the Prize? Sum 3a + b for each machine that has a solution.