Combinatorial dream

\[\large{\sum _{ x=0 }^{ 2010 }{ { \left( -1 \right) }^{ x }\left( \begin{matrix} 2010 \\ 209+x \end{matrix} \right) } \left( \begin{matrix} x+12 \\ x \end{matrix} \right) \pmod{ 1000}} = \, ? \]

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