2015 welcomes Kishlaya's Identity!

Calculus Level 5

Let \[P(n) = \sum_{m=1}^\infty \left(\prod_{k=0}^n \frac{1}{m+k}\right)\] And \[Q(n) = \sum_{k=1}^n \frac{1}{P(k)}\]

Then find the last \(4\) digits of \(Q(2015)+2015\)

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