2010 Cayley Problem 25

Steve places a counter at 0 on the diagram. On his first move, he moves the counter 1^1 step clockwise to 1. On his second move, he moves 2^2 steps clockwise to 5. On his third move, he moves 3^3 steps clockwise to 2. He continues in this manner, moving n^n steps clockwise on his nth move. At which position will the counter be after 1234 moves?

\textbf{(A)}\ 1\quad \textbf{(B)}\ 3\quad \textbf{(C)}\ 5\quad \textbf{(D)}\ 7\quad \textbf{(E)}\ 9

If there are no answer choices shown, enter a numerical answer.

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