2000 Fermat Problem 22

The left most digit of an integer of length 2000 digits is 3. In this integer, any two consecutive digits must be divisible by 17 or 23. The 2000th digit may be either 'a' or 'b'. What is the value of a+b?

\textbf{(A)}\ 3\quad \textbf{(B)}\ 7\quad \textbf{(C)}\ 4\quad \textbf{(D)}\ 10\quad \textbf{(E)}\ 17

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