$($Extra credit $20$ pts$)$ Given some positive integer $k,$ we define the following languages:

a$)$ is a $TM$ and $|L(M)|=k$

b$)$ is a TM and $|L(M)|>k$

For each of these two languages, choose which one of the following classes they belong to$,$ and formally

justify your choice:

i$)$ decidable

ii$)$ Turing$-$recognizable but not co$-$Turing$-$recognizable

iii$)$ co$-$Turing$-$recognizable but not Turing$-$recognizable

iv$)$ neither Turing$-$recognizable nor co$-$Turing$-$recognizable