Chosen Ciphertext Attack textbook RSA

I’m trying to perform a chosen-ciphertext attack against an RSA oracle.
I have $c$ as the ciphertext I want to decrypt, $e$ and $n$.
I already know that I could choose a number $r$, compute $r^e cdot c$, make the oracle decrypt, and return $rcdot m$.

The problem is that this particular oracle checks if $m bmod mo = 0$ where $m$ is the decrypted ciphertext I sent and $mo$ is the original message which I’m trying to get. If it’s equal to $0$ (like $rn$) it won’t print $m$ so I can’t use that attack.

I don’t really know what to do.

$n$ is pretty big (1024bit) so I can’t factorize it. Maybe there is a small adjustment to the mentioned attack, but I’m really stuck. If anybody could give me a hint I would really love it.