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The Floor's Revenge

Problem 546 Published on Sunday, 7th February 2016, 01:00 am; Solved by 158;
Difficulty rating: 85%

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

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

Find $(\sum_{k=2}^{10}$ fk(1014)$)$ mod (109+7).