2004 Pascal Problem 24

In the sequence of fractions \frac{1}{1}, \frac{2}{1}, \frac{1}{2}, \frac{3}{1}, \frac{2}{2}, \frac{1}{3}, \frac{4}{1}, \frac{3}{2}, \frac{2}{3}, \frac{1}{4}, \frac{5}{1}, \ldots, fractions equivalent to any given fraction occur many times. For example, fractions equivalent to \frac{1}{2} occur for the first two times in positions 3 and 14. In which position is the fifth occurrence of a fraction equivalent to \frac{3}{7}?

\textbf{(A)}\ 1207\quad \textbf{(B)}\ 1208\quad \textbf{(C)}\ 1209\quad \textbf{(D)}\ 1210\quad \textbf{(E)}\ 1211

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

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.