KMO 2005 Problem 3

For a positive integer $K$ , define a sequence, $\{a_n\}_n$ , as following $a_1=K$ , $$a_{n+1} = \{ \begin{array} {cc} a_n-1 , & \text{ if } a_n \text{ is even} \frac{a_n-1}2 , & \text{ if } a_n \text{ is odd} \end{array},$$ for all $n\geq 1$ .

Find the smallest value of $K$ , which makes $a_{2005}$ the first term equal to 0.