There is a board game with $N+1$ squares: square $0$, square $1$, $\dots$, square $N$.  
You have a die (dice) that rolls an integer between $1$ and $K$, inclusive, with equal probability for each outcome.  
You start on square $0$. You repeat the following operation until you reach square $N$:

-   Roll the dice. Let $x$ be the current square and $y$ be the rolled number, then move to square $\min(N, x + y)$.

Let $P_i$ be the probability of reaching square $N$ after exactly $i$ operations. Calculate $P_1, P_2, \dots, P_N$ modulo $998244353$.

What is probability modulo $998244353$? It can be proved that the sought probabilities will always be rational numbers. Under the constraints of this problem, it can also be proved that when expressing the values as $\frac{P}{Q}$ using two coprime integers $P$ and $Q$, there is exactly one integer $R$ satisfying $R \times Q \equiv P\pmod{998244353}$ and $0 \leq R < 998244353$. Find this $R$.

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

```
$N$ $K$
```

Print $N$ lines. The $i$-th line should contain $P_i$ modulo $998244353$.

-   $1 \leq K \leq N \leq 2 \times 10^5$
-   $N$ and $K$ are integers.

0
249561089
748683265

For example, you reach square N after exactly two operations when the die rolls the following numbers:

• A 1 on the first operation, and a 2 on the second operation.
• A 2 on the first operation, and a 1 on the second operation.
• A 2 on the first operation, and a 2 on the second operation.

Therefore, $P_2=(\frac{1}{2}\times \frac{1}{2})\times 3=\frac{3}{4}$. We have 249561089×4≡3(mod 998244353), so print 249561089 for $P_2$.