RSA Challenge Three (a): RSA Modulus Reuse

The Problem: Given two RSA ciphertexts of the same message encrypted with the same modulus but different public keys, recover the plaintext.

Awfulland and Badland keep making strange choices with their keys - both of them are using the same modulus, even though their public keys are different. Horridland has formed a new attack plan, and is sending an encrypted copy of the plan to Awfulland and Badland. You've gotten a copy of both encrypted messages:

Awfulland's message, encrypted as c_A = m^e_A mod N (using Awfulland's public exponent e_A), and
Badland's message, encrypted as c_B = m^e_B mod N (using Badland's public exponent e_B).

Use the fact that both copies of the message are encrypted using the same modulus to figure out what the evil plot is.

For this exercise, use the following values:

Name	Value
Common modulus:	153380639740849
Ciphertext #1	106230071531067
Exponent #1	1745
Ciphertext #2	51206346831694
Exponent #2	57