The value of  cos $\frac{\mathrm{\pi }}{65}\cos \frac{2\mathrm{\pi }}{65}\cos \frac{4\mathrm{\pi }}{65}\dots \cos \frac{32\mathrm{\pi }}{65}$is $\frac{k}{320} then k=$

$\cos \frac{\mathrm{\pi }}{65}\cos \frac{2\mathrm{\pi }}{65}\dots \cos \frac{32\mathrm{\pi }}{65}=\cos \frac{\mathrm{\pi }}{65}\cdot \cos \frac{2\mathrm{\pi }}{65}\dots \cos \frac{2^5\mathrm{\pi }}{65}$

$\begin{array}{r}=\frac{\sin \frac{2^6\mathrm{\pi }}{65}}{2^6\sin \frac{\mathrm{\pi }}{65}}=\frac{\sin \frac{64\mathrm{\pi }}{65}}{64\sin \frac{\mathrm{\pi }}{65}}\\ =\frac{\sin \left(\mathrm{\pi }-\frac{\mathrm{\pi }}{65}\right)}{64\sin \frac{\mathrm{\pi }}{65}}=\frac{1}{64}\end{array}$