MathNet 2009-part-02 — 175 problems (EN–VI) Question 149

Let $\{1, 2, \ldots, 2009\} \supseteq A = \{a_1, \ldots, a_k\}$. Find all $A$ sets such that $2009 \mid \sum_{i=1}^{k} a_i$.
(proposed by B. Bayasgalan)