A13164 | 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](https://en.wikipedia.org/wiki/Expected_value) 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 $0 \le x < M$ and $x \cdot q \equiv p \pmod{M}$ .

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.

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