@anton: Hmm, come to think of it, I don’t know where I got the word hacky. I apologise, you said cumbersome though.
And yes, the linear bound on the number of points on the convex hull of all possible movements of A I did not know about, I knew there was a linear bound when n=k though.
Also, there is a tonne of crap in my solution cuz I was trying to fix things that were not incorrect cuz I was making that overflow error. If you would like, I could tidy up my solution and comment it.