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If \( f(x)=\left\{\begin{array}{cc}\frac{1-\sin x}{(\pi-2 x)^{2}} \cdot \frac{\log \sin x}{\left(\log \left(1+\pi^{2}-4 \pi x+4 x^{2}\right)\right.}, & x \neq \frac{\pi}{2} \\ k, & x=\frac{\pi}{2}\end{array}\right. \) is continuous at \( x=\frac{\pi}{2} \), then \( k= \)
(a) \( -\frac{1}{16} \)
(b) \( -\frac{1}{32} \)
(c) \( -\frac{1}{64} \)
(d) \( -\frac{1}{28} \)
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