Alice decides to set up an RSA public key encryption using the two primes $p=31$ and $q=41$ and the encryption key $e=11.$ You must show all calculations, including MOD$-$calculations using the division algorithm!

$(1)[4$pts$]$ Bob decides to send the message $M=30$ to her using this encryption. What is the code $C$ that he will send her?

$(2)[4$pts$]$ What is Alice's decryption key $d?$ Remember that you have to show all your work using the Euclidean algorithm.

$(3)[3$pts$]$ Alice also receives the message $C=101$ from Carla. What was her original message $M?$