Clever Yet Simple Polynomial Subsitution

Algebra Level 4

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

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

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