Let $M=(K,,,s,\{h\}),$ where $K=\{q_0,q_1,h\},=\{a,b,,vv\},s=q_0,$ where $h$ is the halt state, and $$ is given by the following table.

$\backslash$table$[[$q$,\backslash$sigma $,\backslash$delta $($q$,\backslash$sigma $)],[$q$\_(0),$a$,($q$\_(1),$b$)],[$q$\_(0),$b$,($q$\_(1),$a$)],[$q$\_(0),,($h$,)],[$q$\_(0),,($q$\_(0),->)],[$q$\_(1),$a$,($q$\_(0),->)],[$q$\_(1),$b$,($q$\_(0),->)],[$q$\_(1),,($q$\_(0),->)],[$q$\_(1),,($q$\_(1),->)]]$

$($a$)$ Trace the computation of $M$ starting from the initial configuration $(q_0,vv{a}_a$bbba$).$

$($b$)$ Describe what $M$ does to the input string.