Construct a Turing Machine to compute the following function:
$$f(x,y) = 1 \text{ if length(x) > length(y)} \\ =0 \text{ otherwise}{}$$
where $x$ and $y$ are strings over the alphabet set $\{a b\}$. The output should be written on the tape after a \$. For example, if input is $\$abaab\$aaba$, then output should be $\$abaab\$aaba\$1$