\[\large\dbinom{2003}1+\dbinom{2003}4+\dbinom{2003}7+\ldots+\dbinom{2003}{2002}=k(2^{2002}-1)\]

If the value of \(k\) can be represented by \(\dfrac{a}{b}\) when \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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