Training

Ashley is training for a programming contest on Brandon's Online Judge. The judge has a new feature that lets Ashley's coach, Tom, load a list of problems for her.

Each problem has two integers, a lower skill bound $l$ and an upper skill bound $r$. Each programmer has an integer skill level. If a programmer whose skill level is between $l$ and $r$ (inclusive) solves the problem, their skill level goes up by $1$.

Ashley trains on Tom's list in the order Tom loaded the problems. For each problem, she either solves it or skips it. Once she skips a problem, she cannot go back to it.

Compute the maximum skill level Ashley can have if she chooses to solve or skip problems optimally.

The first line contains two integers $n$ and $s$ ($1 \le n \le 10^5$, $0 \le s \le 10^9$), where $n$ is the number of problems and $s$ is Ashley's current skill level.

Each of the next $n$ lines contains two integers $l$ and $r$ ($0 \le l \le r \le 2 \cdot 10^9$), the lower and upper skill bounds of a problem, in the order Tom loaded them.

Output a single integer, the maximum skill level Ashley can attain.