Alice and Bob are conducting Diffie$-$Hellman key exchange with the parameters p$=181$

and $\backslash$alpha $=2$

$.$

Their parameters are small and we decide to crack the key exchange.

Suppose Alice is observed sending public key A$=11$

and Bob sends public key B$=86$

$.$

a$)$ What is Alice's private key?

b$)$ What is Bob's private key?

c$)$ What is the shared secret?