Fraction decomposition

There is a smallest $n$ for which there exists a set of distinct integers $S=\{s_1,s_2,\dots ,s_n\}$ such as
$\frac{17}{670}=(1-\frac{1}{s_1})\times (1-\frac{1}{s_2})\times \cdots \times (1-\frac{1}{s_n})$

Actually, for this least n the set S is unique.

You are given that S is composed of the union of no more than 4 subsets of consecutive integers.

Find S

Answer format: 'the smallest element'-'the largest element' comma separated for each subset.

For instance, if $S=\{2,3,4,5,11,12,13\}=\{2,3,4,5\}\cup \{11,12,13\}$, the answer would be: 2-5,11-13

[My timing: 2 sec ]