Problem Statement

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 $R$.

Constraints

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

Input

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

N K

Output

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