elementary number theory - An easy way to calculate $12^{101} bmod 551$?

We learn about encryption methods, and in one of the exercises we need to calculate: $12^{101} \bmod 551$.

There an easy way to calculate it?
We know that: $M^5=12 \mod 551$
And $M^{505}=M$ ($M\in \mathbb{Z}_{551}$).

(Our goal is to find $M$).
I try to use Fermat, Euler but they can't help me here, right?

P.S. - The idea is to calculate it without calculator...

Thank you!