Function \(f: \mathbb {R \to R}\) satisfies

\[\large f(x) + f \left(1-\frac 1x\right) = 1+x \]

for \(x \ne 0\) and \(x \ne 1\). Then \(2017 - 2f(2017) = \dfrac 1{k(k-1)}\), where \(k\) is a positive integer. Find \(k\).

A corrected problem from Priyanshu Mishra.

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