2003 Combination Sum

Probability Level 4

(20031)+(20034)+(20037)++(20032002)=k(220021)\large\dbinom{2003}1+\dbinom{2003}4+\dbinom{2003}7+\ldots+\dbinom{2003}{2002}=k(2^{2002}-1)

If the value of kk can be represented by ab\dfrac{a}{b} when aa and bb are coprime positive integers, find a+ba+b.

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