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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分