Contest Duration: - (local time) (100 minutes) Back to Home
E - Critical Hit /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

モンスターの体力が 0 以下になるまでに行う攻撃回数の期待値を \text{mod } 998244353 で出力してください（注記参照）。

### 制約

• 1 \leq N \leq 2\times 10^5
• 0 \leq P \leq 100
• 入力は全て整数

### 入力

N P


### 入力例 1

3 10


### 出力例 1

229596204


• 最初、モンスターの体力は 3 です。
• 1 回目の攻撃の後、\frac{9}{10}の確率でモンスターの体力は 2\frac{1}{10}の確率でモンスターの体力は 1 となります。
• 2 回目の攻撃の後、\frac{81}{100}の確率でモンスターの体力は 1\frac{18}{100} の確率でモンスターの体力は 0\frac{1}{100} の確率でモンスターの体力は -1 となります。 \frac{18}{100}+\frac{1}{100}=\frac{19}{100} の確率で体力は 0 以下となり、高橋君は 2 回で攻撃をやめます。
• 2 回目の攻撃の後で体力が 1 残っている場合、3 回目の攻撃の後でモンスターの体力は必ず 0 以下となり、高橋君は 3 回で攻撃をやめます。

よって、期待値は 2\times \frac{19}{100}+3\times\left(1-\frac{19}{100}\right)=\frac{281}{100} となります。229596204 \times 100 \equiv 281\pmod{998244353} であるため、229596204 を出力します。

### 入力例 2

5 100


### 出力例 2

3


### 入力例 3

280 59


### 出力例 3

567484387


Score : 500 points

### Problem Statement

There is a monster with initial stamina N.
Takahashi repeatedly attacks the monster while the monster's stamina remains 1 or greater.

An attack by Takahashi reduces the monster's stamina by 2 with probability \frac{P}{100} and by 1 with probability 1-\frac{P}{100}.

Find the expected value, modulo 998244353 (see Notes), of the number of attacks before the monster's stamina becomes 0 or less.

### Notes

We can prove that the sought expected value is always a finite rational number. Moreover, under the Constraints of this problem, when the value is represented as \frac{P}{Q} by two coprime integers P and Q, we can show that there exists a unique integer R such that R \times Q \equiv P\pmod{998244353} and 0 \leq R \lt 998244353. Print such R.

### Constraints

• 1 \leq N \leq 2\times 10^5
• 0 \leq P \leq 100
• All values in the input are integers.

### Input

The input is given from Standard Input in the following format:

N P


### Output

Find the expected value, modulo 998244353, of the number of Takahashi's attacks.

### Sample Input 1

3 10


### Sample Output 1

229596204


An attack by Takahashi reduces the monster's stamina by 2 with probability \frac{10}{100}=\frac{1}{10} and by 1 with probability \frac{100-10}{100}=\frac{9}{10}.

• The monster's initial stamina is 3.
• After the first attack, the monster's stamina is 2 with probability \frac{9}{10} and 1 with probability \frac{1}{10}.
• After the second attack, the monster's stamina is 1 with probability \frac{81}{100}, 0 with probability \frac{18}{100}, and -1 with probability \frac{1}{100}. With probability \frac{18}{100}+\frac{1}{100}=\frac{19}{100}, the stamina becomes 0 or less, and Takahashi stops attacking after two attacks.
• If the stamina remains 1 after two attacks, the monster's stamina always becomes 0 or less by the third attack, so he stops attacking after three attacks.

Therefore, the expected value is 2\times \frac{19}{100}+3\times\left(1-\frac{19}{100}\right)=\frac{281}{100}. Since 229596204 \times 100 \equiv 281\pmod{998244353}, print 229596204.

### Sample Input 2

5 100


### Sample Output 2

3


Takahashi's attack always reduces the monster's stamina by 2. After the second attack, the stamina remains 5-2\times 2=1, so the third one is required.

### Sample Input 3

280 59


### Sample Output 3

567484387