CF1264C.Beautiful Mirrors with queries

Creatnx has $n$ mirrors, numbered from $1$ to $n$. Every day, Creatnx asks exactly one mirror "Am I beautiful?". The $i$-th mirror will tell Creatnx that he is beautiful with probability $\frac{p_i}{100}$ for all $1 \le i \le n$.

Some mirrors are called checkpoints. Initially, only the $1$st mirror is a checkpoint. It remains a checkpoint all the time.

Creatnx asks the mirrors one by one, starting from the $1$-st mirror. Every day, if he asks $i$-th mirror, there are two possibilities:

• The $i$-th mirror tells Creatnx that he is beautiful. In this case, if $i = n$ Creatnx will stop and become happy, otherwise he will continue asking the $i+1$-th mirror next day;
• In the other case, Creatnx will feel upset. The next day, Creatnx will start asking from the checkpoint with a maximal number that is less or equal to $i$.

There are some changes occur over time: some mirrors become new checkpoints and some mirrors are no longer checkpoints. You are given $q$ queries, each query is represented by an integer $u$: If the $u$-th mirror isn't a checkpoint then we set it as a checkpoint. Otherwise, the $u$-th mirror is no longer a checkpoint.

After each query, you need to calculate the expected number of days until Creatnx becomes happy.

Each of this numbers should be found by modulo $998244353$. Formally, let $M = 998244353$. It can be shown that the answer can be expressed as an irreducible fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \not \equiv 0 \pmod{M}$. Output the integer equal to $p \cdot q^{-1} \bmod M$. In other words, output such an integer $x$ that $0 \le x \lt M$ and $x \cdot q \equiv p \pmod{M}$.

Creatnx 有 $n$ 面镜子，编号从 $1$ 到 $n$。每天，Creatnx 恰好向一面镜子提问：“我漂亮吗？”。第 $i$ 面镜子以概率 $\frac{p_i}{100}$ 回答 Creatnx“你很漂亮”，其中 $1 \le i \le n$。

某些镜子被称为检查点（checkpoints）。初始时，仅有第 $1$ 面镜子是检查点，并且它将永远保持为检查点。

Creatnx 每天按顺序向镜子提问，从第 $1$ 面镜子开始。若某天他向第 $i$ 面镜子提问，则有两种可能：

• 第 $i$ 面镜子回答“你很漂亮”。此时，若 $i = n$，则 Creatnx 停止提问并变得开心；否则，他将在第二天继续向第 $i+1$ 面镜子提问；
• 否则（即镜子未说他漂亮），Creatnx 会感到沮丧。第二天，他将从所有编号不超过 $i$ 的检查点中，选择编号最大的那个作为起点重新开始提问。

过程中会发生若干变化：某些镜子会成为新的检查点，而另一些镜子则不再作为检查点。你将收到 $q$ 个查询，每个查询由一个整数 $u$ 表示：若第 $u$ 面镜子当前不是检查点，则将其设为检查点；否则，将其取消为检查点。

每次查询后，你需要计算 Creatnx 变得开心所需的期望天数。

每个答案需对 $998244353$ 取模。形式化地，令 $M = 998244353$。可以证明该期望值可表示为既约分数 $\frac{p}{q}$，其中 $p$ 和 $q$ 为整数，且 $q \not \equiv 0 \pmod{M}$。请输出整数 $p \cdot q^{-1} \bmod M$。换言之，输出满足 $0 \le x < M$ 且 $x \cdot q \equiv p \pmod{M}$ 的唯一整数 $x$。

The first line contains two integers $n$, $q$ ($2 \leq n, q \le 2 \cdot 10^5$) — the number of mirrors and queries.

The second line contains $n$ integers: $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq 100$).

Each of $q$ following lines contains a single integer $u$ ($2 \leq u \leq n$) — next query.

第一行包含两个整数 $n$、$q$（$2 \leq n, q \le 2 \cdot 10^5$）—— 分别表示镜子的数量和查询次数。

第二行包含 $n$ 个整数：$p_1, p_2, \ldots, p_n$（$1 \leq p_i \leq 100$）。

接下来的 $q$ 行中，每行包含一个整数 $u$（$2 \leq u \leq n$）—— 表示下一个查询。

Print $q$ numbers – the answers after each query by modulo $998244353$.

输出 $q$ 个数——每次查询后的答案对 $998244353$ 取模的结果。

In the first test after the first query, the first and the second mirrors are checkpoints. Creatnx will ask the first mirror until it will say that he is beautiful, after that he will ask the second mirror until it will say that he is beautiful because the second mirror is a checkpoint. After that, he will become happy. Probabilities that the mirrors will say, that he is beautiful are equal to $\frac{1}{2}$. So, the expected number of days, until one mirror will say, that he is beautiful is equal to $2$ and the answer will be equal to $4 = 2 + 2$.

在第一次查询后的第一次测试中，第一面和第二面镜子是检查点。Creatnx 将持续询问第一面镜子，直到它说他很美；之后，由于第二面镜子是一个检查点，他将持续询问第二面镜子，直到它说他很美；此后，他便会变得开心。每面镜子说他很美的概率均为 $\frac{1}{2}$。因此，直到某一面镜子说他很美所需的期望天数为 $2$，故答案为 $4 = 2 + 2$。