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}).