ChthollyNotaSeniorious gives DataStructures a number axis with $$$m$$$ distinct segments on it. Let $$$f(l,r)$$$ be the number of ways to choose an even number of segments such that the union of them is exactly $$$[l,r]$$$, and $$$g(l,r)$$$ be the number of ways to choose an odd number of segments such that the union of them is exactly $$$[l,r]$$$.
ChthollyNotaSeniorious asked DataStructures $$$q$$$ questions. In each query, ChthollyNotaSeniorious will give DataStructures two numbers $$$l, r$$$, and now he wishes that you can help him find the value $$$f(l,r)-g(l,r)$$$ modulo $$$998\,244\,353$$$ so that he wouldn't let her down.
The first line of input contains two integers $$$m$$$ ($$$1 \leq m \leq 2 \cdot 10^5$$$) and $$$q$$$ ($$$1 \leq q \leq 2 \cdot 10^5$$$) — the number of segments and queries, correspondingly.
The $$$i$$$-th of the next $$$m$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \leq x_i < y_i \leq 10^9$$$), denoting a segment $$$[x_i, y_i]$$$.
It is guaranteed that all segments are distinct. More formally, there do not exist two numbers $$$i, j$$$ with $$$1 \le i < j \le m$$$ such that $$$x_i = x_j$$$ and $$$y_i = y_j$$$.
The $$$i$$$-th of the next $$$q$$$ lines contains two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \leq l_i < r_i \leq 10^9$$$), describing a query.
For each query, output a single integer — $$$f(l_i,r_i)-g(l_i,r_i)$$$ modulo $$$998\,244\,353$$$.
4 2 1 3 4 6 2 4 3 5 1 4 1 5
1 0
In the first query, we have to find $$$f(1, 4) - g(1, 4)$$$. The only subset of segments with union $$$[1, 4]$$$ is $$$\{[1, 3], [2, 4]\}$$$, so $$$f(1, 4) = 1, g(1, 4) = 0$$$.
In the second query, we have to find $$$f(1, 5) - g(1, 5)$$$. The only subsets of segments with union $$$[1, 5]$$$ are $$$\{[1, 3], [2, 4], [3, 5]\}$$$ and $$$\{[1, 3], [3, 5]\}$$$, so $$$f(1, 5) = 1, g(1, 5) = 1$$$.
