Power matters!

Algebra Level pending

Let p(x) be a polynomial with degree 2009 and leading co-efficient unity such that p(0)=2008 ; p(1)=2007; p(2)=2006...
. p(2008)=0 and the value of p(2009)= (n!)-a
here a and n are natural numbers.
then the value of n+a is?
\[n!=1X2X3X4X.....n \]

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