Suppose that machine M$1$ recognizes abc exactly, and machine M$2$ recognizes bcb exactly. Further suppose that the machines M$1$ and M$2$ are put into a larger machine M$.$ M$1$ has states s$1,$ s$2,...$ s$5,$ and M$2$ has states t$1,$ t$2,...,$ t$7.$ Because these inputs are given to M$,$ they are passed to M$1$ until M$1$ enters an accepting state and the remainders are then passed to M$2.$ Finally, if M$2$ enters the accepting state, one will say that M accepts the input.

How many states does M have?

$7$

$5$

$12$

$5^7$