D. Segments Coveringtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere is a linear strip divided into $$$m$$$ cells, numbered from $$$1$$$ to $$$m$$$ from left to right.You are given $$$n$$$ segments. Each segment is defined by four numbers: $$$l$$$, $$$r$$$, $$$p$$$ and $$$q$$$ — the segment covers cells from $$$l$$$ to $$$r$$$ inclusively and exists with probability $$$\frac{p}{q}$$$ (independently).Your task is to calculate the probability that each cell is covered by exactly one segment.InputThe first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 2 \cdot 10^5$$$).Then $$$n$$$ lines follow. The $$$i$$$-th of them contains four integers $$$l_i$$$, $$$r_i$$$, $$$p_i$$$ and $$$q_i$$$ ($$$1 \le l_i \le r_i \le m$$$; $$$1 \le p_i < q_i < 998244353$$$).OutputPrint a single integer — the probability that each cell is covered by exactly one segment, taken modulo $$$998244353$$$.Formally, the probability can be expressed as an irreducible fraction $$$\frac{x}{y}$$$. You have to print the value of $$$x \cdot y^{-1} \bmod 998244353$$$, where $$$y^{-1}$$$ is an integer such that $$$y \cdot y^{-1} \bmod 998244353 = 1$$$.ExamplesInput3 31 2 1 33 3 1 21 3 2 3Output610038216
Input2 31 2 1 22 3 1 2Output0
Input8 51 3 1 21 5 1 61 4 4 55 5 1 74 5 1 24 5 2 53 3 2 71 2 1 3Output94391813
NoteIn the first example, the probability is equal to $$$\frac{5}{18}$$$.