Universal and Existential Quantifiers

You are given a list of $N$ intervals. The $i$-th interval is $\[l_i,r_i)$, which denotes the range of numbers greater than or equal to $l_i$ and strictly less than $r_i$. In this task, you consider the following two numbers:

• The minimum integer $x$ such that you can select $x$ intervals from the given $N$ intervals so that the union of the selected intervals is $\[0,L)$.
• The minimum integer $y$ such that no matter how you choose $y$ intervals from the given $N$ intervals, the chosen intervals cover $\[0,L)$.

Write a program to compute these two numbers.

The input consists of a single test case formatted as follows.

The first line contains two integers $N$ ($1 \le N \le 2 \cdot 10^5$) and $L$ ($1 \le L \le 10^{12}$), where $N$ is the number of intervals and $L$ is the length of the range to be covered. The $i$-th of the following $N$ lines contains two integers $l_i$ and $r_i$ ($0 \le l_i < r_i \le L$), representing the range of the $i$-th interval $\[l_i,r_i)$. You can assume that the union of all the $N$ intervals is $\[0,L)$.

Output the two integers $x$ and $y$ defined in the problem statement, separated by a single space, on one line.