# Clever Yet Simple Polynomial Subsitution

Algebra Level 3

Let $$f(x)$$ be a monic polynomial of degree $$2009$$ such that $$f(m) = 1$$ for $$m = 1, 2, 3,\cdots,2009$$. Find $$2010(f(2010)-2009!)$$.

Note that monic means that the leading coefficient of the polynomial is 1.

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