Let \(p(x)\) be a polynomial of \(2015^\text{th}\) degree. We know that for every integer \(k\) with \(2 \le k \le 2017\): \[ \large p(k) = \frac{k}{k^2-1}. \]

Find the value of \(p(2018)\). If this value can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, submit your answer as \(b\).

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