Cannonball

Bessie has mastered the art of turning into a cannonball and bouncing along a number line of length $N$ ($1 \leq N \leq 10^5$) with locations numbered $1, 2, \dots, N$ from left to right. She starts at integer location $S$ ($1 \leq S \leq N$) bouncing to the right with a starting power of 1. If Bessie has power $k$, her next bounce lands at a distance $k$ forward from her current location.

Every integer location from 1 to $N$ is either a target or a jump pad. Each target and jump pad has an integer value from 0 to $N$ inclusive. A jump pad with value $v$ increases Bessie's power by $v$ and reverses her direction. A target with value $v$ breaks if Bessie lands on it with a power of at least $v$. Landing on a target does not change her power or direction. A broken target stays broken, and Bessie can still bounce on it without changing power or direction.

If Bessie bounces forever or until she leaves the number line, how many targets will she break?

If Bessie starts on a target she can break, she breaks it immediately. Likewise, if she starts on a jump pad, the pad's effect applies before her first jump.

The first line contains $N$ and $S$, where $N$ is the length of the number line and $S$ is Bessie's starting location.

The next $N$ lines describe each location. The $i$-th line contains integers $q_i$ and $v_i$, where $q_i = 0$ if location $i$ is a jump pad and $q_i = 1$ if location $i$ is a target, and $v_i$ is the value of location $i$.

Output one number, the number of targets that will be broken.