It is much easier than expected: you know that you can reach at most a Manhattan distance of s steps, and that, going randomly, you might have x steps that nullify x steps in the opposite direction.

So, if I had the chance to move by, say, 5 steps, I could end up to places like [0,5], [0,-5], [5,0] or [-5,0] moving in a straight line, [3,2] or [-1,4] combining direction or, having some backtracking, in places like [0,1] or [-1,2], but I would never be able to reach [2,2] or [0,-4] in 5 steps.

Hope this helps, cheers :)