Modular exponentiation

Modular exponentiation is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Find the last 20 decimal digits of $a^{b}$, where

• $a=2988348162058574136915891421498819466320163312926952423791023078876139$
• $b=2351399303373464486466122544523690094744975233415544072992656881240319$

A computer is too slow to find the entire value of $a^{b}$. Instead, the program must use a fast algorithm for modular exponentiation: $a^{b}\mod m$.

The algorithm must work for any integers $a,b,m$ where $b\geq 0$ and $m\neq 0$.