elementary number theory - More than one modular multiplicative inverse possible?

I am redoing exams as a preparation and I found this weird particular exercise to me.

"Does $32$ have a multiplicative inverse in modulo $77$? If yes, calculate the inverse."

Since the $\gcd(77,32)$ is $1$, it has an inverse.
However, when I calculated it using the extended euclidean algorithm, I ended up with

$1 = (-12)32 + (5)77$, which means my inverse of $32$ in mod $77$ is $-12$?
When I used an online calculator to check my answer I always got $65$, though.

I'm not quite sure I understand why or how it is $65$ and not $-12$...
I have redone my method multiple times but I always end up with $-12$

Thank you for your time in advance.