Cow Jog

The cows are out exercising their hooves again. $N$ cows are jogging on an infinitely long single-lane track ($1 \le N \le 100\,000$). Every cow starts at a different position, and some cows jog at different speeds.

The track has only one lane, so a cow cannot pass the cow ahead of her. When a faster cow catches up to the cow ahead, she slows down to avoid running into her and becomes part of the same group.

The cows run for $T$ minutes ($1 \le T \le 10^9$). Determine how many groups are left at that point. Two cows count as the same group if they are at the same position at the end of the $T$ minutes.

The first line contains the two integers $N$ and $T$.

Each of the next $N$ lines contains the starting position and the speed of one cow. The position is a nonnegative integer and the speed is a positive integer, and both are at most 1 billion. All cows start at different positions, and the positions are given in increasing order.

Print a single integer, the number of groups that remain after $T$ minutes.