M $2=$On input string w:

$1.$ Sweep left to right across the tape, crossing off every other $0.$

$2.$ If in stage $1$ the tape contained a single $0,$ accept.

$3.$ If in stage $1$ the tape contained more than a single $0$ and the

number of $0$s was odd, reject.

$4.$ Return the head to the left$-$hand end of the tape.

$5.$ Go to stage $1.$

In each of the parts, give the sequence of configurations that M $2$ enters when

started on the indicated input string.

a$.0.$

b$.00.$

c$.000.$

d$.000000$