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