Racing Gems

You are playing a racing game. Your character starts on the $x$ axis ($y = 0$) and runs up the track, which is bounded by the line $x = 0$ on one side and by the line $x = w$ on the other. You may start anywhere along the starting line, as long as the position is inside the track. The finish line is $y = h$, and the game ends when you reach it.

Your vertical velocity is fixed at $v$. Your horizontal velocity, on the other hand, can be any value between $-v/r$ and $v/r$, and you may change it at any time.

There is one gem at each of $n$ fixed points on the track. You want to collect as many gems as possible. How many gems can a single run collect?

The first line contains four space separated integers $n$, $r$, $w$, and $h$ ($1 \le n \le 10^5$, $1 \le r \le 10$, $1 \le w, h \le 10^9$).

Each of the next $n$ lines contains two space separated integers $x_i$ and $y_i$, the coordinates of the $i$th gem ($0 \le x_i \le w$, $0 < y_i \le h$). No two gems share a position.

The input does not contain a value for $v$.

Print, on a single line, the largest number of gems that can be collected during the race.