Let X = {a, b} and Y = {1, 2, none, both}. Construct a Mealy machine that outputs a 1 if the number of as in the input string (mod 4) is equal to 2, outputs a 2 if the number of bs 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.