How to construct this Moore machine that outputs.... (or prove that it doesn't exist) ?

Let X = {a, b} and Y = {1, 2, none, both}. Construct a Moore machine that outputs a I if the input string has I more a's than b's or 1 less a's than b's; outputs a 2 if the input string has 2 more or 2 less a's than b's; and outputs "none" otherwise. If such a Moore machine does not exist show / prove why not