please don't copy and paste the wrong answer (the other answers to this question are incorrect I believe)

4. Let X = {a, b} and Y = {1, 2, none, both}. Construct a Mealy machine that outputs a 1 if the number of a's in the input string (mod 4) is equal to 2, outputs a 2 if the number of b's in the input string (mod 3) is equal to 1, and outputs "both" if both conditions are true. If neither condition is true it outputs "none." If such a Mealy machine does not exist indicate why not