CF2125D Segments Covering

There 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.

The 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 $ ).

Print 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 $ .

In the first example, the probability is equal to $ \frac{5}{18} $ .