Let $p$ be a constant number such that $0 < p < 1$. Evaluate

\[
\sum_{k=0}^{2004} \frac{p^k (1-p)^{2004-k}}{\int_0^1 x^k (1-x)^{2004-k} \, dx}
\]

Let's think step by step and output the final answer within \boxed{}.
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