In the paillier cryptosystem:

http://en.wikipedia.org/wiki/Paillier_cryptosystem

Suppose that i know a Ciphertext encrypted with some unknown random r i.e.

C = ((g^m) * (r^n)) mod n^2

I know g, n, the prime factorization of n i.e. p*q. I also know the private key - hence i know the message m. Would there be a way for me to recover r easily?