Two-lane Road

Chef works as a cook in a restaurant. Each morning, he has to drive down a straight road with length $K$ to reach the restaurant from his home. Let's describe this road using a coordinate $X$; the position of Chef's home is $X = 0$ and the position of the restaurant is $X = K$. The road has exactly two lanes (numbered $1$ and $2$), but there are $N$ obstacles (numbered $1$ through $N$) on it. For