Construct a Turing machine M $($over alphabet $=\{$a$,$ b$\})$ which will decide the language

A consisting of all strings of length $4$ or greater, having a as their fourth last symbol. More

formally,

A $=\{$xay $|$ x$,$ y in $,|$y$|=3\}.$

For example, abba and bbaaab are in A$,$ but baba and aaa are not. You should present the

Turing machine as a state diagram. You can leave out its reject state, with the understanding

that missing transitions are transitions to the reject state. However, indicate clearly the

initial state q$0$ and the accept state qa$.$