Determine which integers in the set $S :\{-32,-8,16,32\}$ will make the inequality $\frac{1}{4}(m-4) \leq \frac{1}{8}(m-16)$ false.

A$S:\{16, 32\}$

B$S:\{-8,16\}$

C$S:\{-32, -8\}$

D$S:\{-32, 32\}$