RSA is an encryption algorithm where a sender, Bob, sends an encrypted message to a receiver, Alice. The process followed by RSA to create the encryption methods follows a somewhat complex mathematical reasoning that we summarize in the following image:

The first thing Bob does is to generate three values , , and following the four steps shown in the image. Then, he will share and , which allows Alice to encode the message following the formula in box (I). For example, if Alice wants to send the message and we have that and , the encoded message will be . That is, Alice sends over the channel (II). After that Bob, who is the only one who knows (in this case ), applies the decoding formula, obtains that , which matches the desired message (III).

If a third person intercepts the channel, they still won't know since it is not shared, so they will not be able to decode even if they have access to it.

Create a function that, given two primes and returns valid values of , and .