A Professor generated two pairs of RSA keys for his tutors, using a pair of p and q

A Professor generated two pairs of RSA keys for his tutors, using a pair of p and q. The chosen public component e1 and e2 are different prime numbers. Both p and q are very large prime numbers and were destroyed immediately after generating the following keys: Person A: < n, e1 >, < n, d1 > Person B: < n, e2 >, < n, d2 >
Answer the following questions with detailed process and/or justification.
(a) Person C wants to send a confidential message M to both A and B, so he calculates and then sends C1 = Me1 mod n and C2 = Me2 mod n. Explain how you may recover this message without knowing A's or B's private key.
(b) Outline a strategy that may help B recover A's private key.