CF1392H.ZS Shuffles Cards

zscoder has a deck of $n+m$ custom-made cards, which consists of $n$ cards labelled from $1$ to $n$ and $m$ jokers. Since zscoder is lonely, he wants to play a game with himself using those cards.

Initially, the deck is shuffled uniformly randomly and placed on the table. zscoder has a set $S$ which is initially empty.

Every second, zscoder draws the top card from the deck.

• If the card has a number $x$ written on it, zscoder removes the card and adds $x$ to the set $S$.
• If the card drawn is a joker, zscoder places all the cards back into the deck and reshuffles (uniformly randomly) the $n+m$ cards to form a new deck (hence the new deck now contains all cards from $1$ to $n$ and the $m$ jokers). Then, if $S$ currently contains all the elements from $1$ to $n$, the game ends. Shuffling the deck doesn't take time at all.

What is the expected number of seconds before the game ends? We can show that the answer can be written in the form $\frac{P}{Q}$ where $P, Q$ are relatively prime integers and $Q \neq 0 \bmod 998244353$. Output the value of $(P \cdot Q^{-1})$ modulo $998244353$.

zscoder 有一副由 $n+m$ 张特制卡片组成的牌组，其中包括 $n$ 张编号为 $1$ 到 $n$ 的卡片和 $m$ 张小丑牌（joker）。由于 zscoder 感到孤独，他想用这些卡片独自进行一场游戏。

初始时，这副牌被均匀随机地洗牌，并放置在桌面上。zscoder 拥有一个集合 $S$，其初始为空集。

每过一秒，zscoder 从牌组顶部抽出一张牌：

• 若抽出的牌上写有数字 $x$，则 zscoder 移除该牌，并将 $x$ 加入集合 $S$；
• 若抽出的牌是一张小丑牌，则 zscoder 将所有已移除的卡片（即当前不在 $S$ 中、但尚未被重新放入牌组的牌）全部放回牌组，并对全部 $n+m$ 张卡片（即编号 $1$ 至 $n$ 的卡片及 $m$ 张小丑牌）进行均匀随机洗牌，从而构成一副新牌组；随后，若此时集合 $S$ 已包含 $1$ 至 $n$ 的所有整数，则游戏结束。洗牌本身不耗费任何时间。

求游戏结束前的期望秒数。可以证明该答案可表示为最简分数形式 $\frac{P}{Q}$，其中 $P, Q$ 为互质整数且 $Q \neq 0 \bmod 998244353$。请输出 $(P \cdot Q^{-1}) \bmod 998244353$ 的值。

The only line of the input contains two integers $n$ and $m$ ($1 \le n, m \le 2 \cdot 10^{6}$).

输入仅包含一行，其中有两个整数 $n$ 和 $m$（$1 \le n, m \le 2 \cdot 10^{6}$）。

Output a single integer, the value of $(P \cdot Q^{-1})$ modulo $998244353$.

输出一个整数，即 $(P \cdot Q^{-1})$ 对 $998244353$ 取模的值。

For the first sample, it can be proven that the expected time before the game ends is $5$ seconds.

For the second sample, it can be proven that the expected time before the game ends is $\frac{28}{3}$ seconds.

对于第一个样例，可以证明游戏结束前的期望时间为 $5$ 秒。

对于第二个样例，可以证明游戏结束前的期望时间为 $\frac{28}{3}$ 秒。