20638번 - Universal and Existential Quantifiers 다국어

You are given a list of $N$ intervals. The $i$-th interval is $[l_i,r_i)$, which denotes a 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 for all possible combinations of $y$ intervals from the given $N$ interval, it does cover $[0,L)$.

We ask you to 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 range to be covered, respectively. 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 two integers $x$ and $y$ mentioned in the problem statement, separated by a single space, in a line.