Suppose that Alice's RSA public key is $($N; e$)$ and her private key is $($N; d$)$ where e is the encryption exponent, d is the decryption exponent, and N is the product of two prime numbers p and q$.$ We are given that p $=3$; q $=11$ and e $=7.$

a$)$ If Bob encrypts the message M $=2$ with the RSA algorithm using Alice's public key, what is the ciphertext C that Bob sends to Alice?

$($b$)$ To show Alice can decrypt C to obtain M$.$