What is the value of $$\left(k -\frac{1}{k}\right)\left(k^{2} + \frac{1}{k^{2}}\right)\left(k^{4} + \frac{1}{k^{4}}\right)\left(k^{8} + \frac{1}{k^{8}}\right)\left(k^{16} + \frac{1}{k^{16}}\right)$$?

A

$$k^{64} - \frac{1}{k^{64}}$$

B

$$\frac{k^{32} - \frac{1}{k^{32}}}{k - \frac{1}{k}}$$

C

$$k^{32} - \frac{1}{k^{32}}$$

D

$$\frac{k^{32} - \frac{1}{k^{32}}}{k + \frac{1}{k}}$$