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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).

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