If $$\frac{1}{2 \cdot 3^{10}} + \frac{1}{2^2 \cdot 3^9} + \cdots + \frac{1}{2^{10} \cdot 3} = \frac{K}{2^{10} \cdot 3^{10}}$$, then the remainder when $$K$$ is divided by $$6$$ is

A

2

B

3

C

4

D

5