Highway

Bob is a skilled engineer. He must design a highway that crosses a region with very few villages. Since this region is sparsely populated, he wants to minimize the number of exits from the highway. He models the highway as a line segment $S$ on the plane from the origin $(0, 0)$ to the point $(L, 0)$, the villages as points on the plane, and the exits as points on $S$. Given the highway and the positions of the villages, Bob must find the minimum number of exits such that every village is at distance at most $D$ from at least one exit. It is guaranteed that every village is at distance at most $D$ from the segment $S$.

The input consists of several data sets; each data set describes one highway and the positions of its villages. A data set starts with the length $L$ (an integer) of the highway. It is followed by the distance $D$ (an integer), the number $N$ of villages, and, for each village, its integer coordinates $(x, y)$. White space may occur freely in the input. The input is always valid and terminates at end of file.

For each data set, print the minimum number of exits on its own line, starting at the beginning of the line.