$1-$a$)$ Describe a deterministic Turing Machine $M$ that accepts inputs of $0\text{'}$s and $1\text{'}$s in which the number of $1\text{'}$s is divisible by $3$ and the number of $0\text{'}$s is a even number $($hint find first a corresponding DFA$).$ The tape symbols are $=\{0,1,b\},$ and the alphabet is $=\{0,1\}$ and the original state is $q_0$ and the halting states are $q_y$ and $q_n.$Describe a deterministic Turing Machine M that accepts inputs of $0$s and $1$s in which the number of $1$s is divisible by $3$ and the number of $0$s is a even number $($hint find first a corresponding DFA$).$ The tape symbols are $\backslash$Gamma $=\{0,1,$b$\},$ and the alphabet is $=\{0,1\}$ and the original state is q$0$ and the halting states are qy and qn$.$