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# Problem 546

The Floor’s Revenge

Define $f_k(n)=\sum^{n}_{i=0}f_k(\lfloor \frac{i}{k} \rloor)$ where $f_k(0)=1$ and $\lfloor x \rfloor$ denotes the floor function.

For example, f5(10) = 18, f7(100) = 1003, and f2(103) = 264830889564.

Find $(\sum^{10}_{k=2}f_k(10^{14})) \text{ mod } (10^9+7)$.