Let \(P(x)\) be a polynomial of degree 2015 which satisfies \(P(k) = 2^{k}\) for all \(k=0,1,2,3, \ldots, 2015\). If the value of \(P(2016)\) can be expressed as

\[a^{b} - c,\]

where \(a\) and \(c\) are coprime integers and \(a\) is a prime, find the value of \(a+b+c\).

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