Very interesting problem that I can't solve.

This was on my grade 10 Cayley math contest a few days ago. It is really interesting, but super hard.

We have a circle with 10 points (think of a clock that goes from 0-9). The dial starts at 0. In each move Tom moves the dial times. So on the first move Tom moves times, and the dial is at 1. Second move Tom moves times, and the dial is at 5, and third move Tom moves times, and the dial is at 2. What number would the dial be pointing at after 1234 moves?

Essentially it is asking what is.