Let \(ABCD\) be a regular tetrahedron and let \(E\) be a point inside the face \(ABC.\) Denote by \(s\) the sum of the distances from \(E\) to the faces \(DAB, DBC, DCA,\) and by \(S\) the sum of the distances from \(E\) to the edges \(AB, BC, CA.\) Find the value of \(\frac{s}{S}\). The original answer is in the form \(\frac{k \sqrt{2}}{m}\), please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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