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Let P(x)P(x)P(x) be a polynomial of degree 2015 which satisfies P(k)=2kP(k) = 2^{k}P(k)=2k for all k=0,1,2,3,…,2015k=0,1,2,3, \ldots, 2015k=0,1,2,3,…,2015. If the value of P(2016)P(2016)P(2016) can be expressed as
ab−c,a^{b} - c,ab−c,
where aaa and ccc are coprime integers and aaa is a prime, find the value of a+b+ca+b+ca+b+c.
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