If $$X + \frac{1}{x} = \frac{K}{2}$$, then what is the value of $$\frac{x^{8} + 1}{x^{4}}$$?

A

$$\frac{K^{4} - 16K^{2} + 32}{16}$$

B

$$\frac{K^{4} - 8K^{2} - 32}{32}$$

C

$$\frac{K^{4} - 8K^{2} - 32}{16}$$

D

$$\frac{K^{4} - 8K^{2} + 32}{16}$$