Problem Statement

You are given an integer $N \geq 2$ and an integer $P$ between $0$ and $100$, inclusive. Let $p=P/100$.

There is a sequence $A$. Initially, the length of $A$ is $1$, and its only element is $1$.

The following operation is repeated $N-1$ times on sequence $A$:

• Let $m$ be the smallest positive integer that does not appear in $A$. With probability $p$, perform operation $1$; with probability $1-p$, perform operation $2$:
• Operation $1$: Append $m$ to the end of $A$.
  • Operation $2$: Let $c_1,c_2,\dots,c_{m-1}$ be the number of times $1,2,\dots,m-1$ appear in $A$, respectively. Choose an integer $k$ between $1$ and $m-1$, inclusive, with probability proportional to $c_k$. That is, choose $k$ with probability $c_k/\sum_{j=1}^{m-1} c_j$. Then, append $k$ to the end of $A$.

For each $k=1,2,\dots,N$, find the expected number of occurrences of $k$ in $A$ after $N-1$ operations, modulo $998244353$.

Definition of expected value modulo $998244353$ It can be proved that the expected value you seek is always a rational number. Also, under the constraints of this problem, it can be proved that when this value is expressed as an irreducible fraction $\frac{P}{Q}$, we have $Q {{}\not\equiv{}} 0 \pmod{998244353}$. Therefore, there is a unique integer $R$ such that $R \times Q \equiv P \pmod{998244353}$ and $0 \leq R \lt 998244353$. Output this $R$.

Constraints

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

Input

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

N P

Output

Output $N$ lines. The $k$-th $(1\leq k \leq N)$ line should contain the expected number of occurrences of $k$ in $A$ after the operations, modulo $998244353$.