Moejy0viiiiiv 在平面直角坐标系上抢红包。从 $(0,0)$ 出发，每天中午有 $A/1996488707$ 的概率向上走一格，有 $B/1996488707$ 的概率向右走一格，有 $1-A/1996488707-B/1996488707$ 的概率立即停止行动（之后也不再行动），三种事件两两不会同时发生；Moejy0viiiiiv 在第 $N$ 天傍晚离开平面直角坐标系（总共至多走 $N$ 格）。

已知一个常数 $D$，在所有 $(xD,yD)(0\le x,y)$ 处有一个红包；还有 $K$ 个坑，分别在 (x1,y1),(x2,y2),(x3,y3),⋯,(xK,yK)(x_1, y_1), (x_2, y_2), (x_3, y_3), \cdots, (x_K, y_K)(x​1​​,y​1​​),(x​2​​,y​2​​),(x​3​​,y​3​​),⋯,(x​K​​,y​K​​)，走入坑中将在接下来的回合中无法行动。

Moejy0viiiiiv 会抢走所有她经过的红包（包含 $(0,0)$）问最终期望抢到的红包数量，输出这个值 $mod998244353$，注意 $1996488707mod998244353=1$。

Moejy0viiiiiv is collecting red envelopes on a rectangular plane. She starts at $(0,0)$. Every day at noon, she walks from $(x,y)$ to $(x,y+1)$ with probability $A/1996488707$, and to $(x+1,y)$ with probability $B/1996488707$, and stops immediately with probability $1-A/1996488707-B/1996488707$ (once she stops, she will never move again). Besides, she also stops after walking for $N$ days.

With a given constant integer $D$, there’s a red envelope at each $(xD,yD)(0\le x,y)$. There’re also $K$ barriers at (x1,y1),(x2,y2),(x3,y3),...,(xK,yK)(x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_K, y_K)(x​1​​,y​1​​),(x​2​​,y​2​​),(x​3​​,y​3​​),...,(x​K​​,y​K​​) (barriers never coincide with red envelopes). If she walks to a barrier, she will stop immediately.

Moejy0viiiiiv will collect each red envelope she passes by (including $(0,0)$). What’s the expected number of red envelopes Moejy0viiiiiv collects after $N$ days? Output the answer $mod998244353$. Notice that $1996488707mod998244353=1$.