$4.$ In each of the following schemes Ek $($m$)=[$m$+$k$($mod $3)].$ State in each case whether the scheme is perfectly secret, and justify your answers.

A$.$ The message space is$.=\{0,1),$ and Gen chooses a uniform key from the key space K$=[0,1].$

B$.$ the message space is$.=[0,1,2),$ and Gen chooses a uniform key from the key space K$=[0,1,2).$

C$.$ The message space is$.=\{0,1],$ and Gen chooses a uniform key from the key space K$=\{0,1,2).$