Cow Jog

Farmer John's $N$ cows are jogging along an infinite track. Cow $i$ starts at position $x_i$ and runs in the same direction at a constant speed of $v_i$ per minute. All starting positions are distinct.

The track is divided into lanes, so cows in different lanes may move past each other. No two cows in the same lane may ever occupy the same position. Farmer John does not want any cow to change lanes or adjust its speed.

The cows run for $T$ minutes. Find the minimum number of lanes he needs. Times from $0$ to $T$ count, including time $T$ itself.

The first line contains the number of cows $N$ and the running time $T$. ($1 \le N \le 10^5$, $1 \le T \le 10^9$)

Each of the next $N$ lines contains the starting position $x_i$ and the speed $v_i$ of one cow. $x_i$ is a nonnegative integer at most $10^9$, and $v_i$ is a positive integer at most $10^9$. All starting positions are distinct and are given in increasing order.

Print one line with the minimum number of lanes needed so that no two cows in the same lane ever occupy the same position up to time $T$.