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.

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.

Constraints

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

Sample Input 1

3 2

Sample Output 1

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, $P_2 = \left( \frac{1}{2} \times \frac{1}{2} \right) \times 3 = \frac{3}{4}$. We have $249561089 \times 4 \equiv 3 \pmod{998244353}$, so print 249561089 for P_2.

Sample Input 2

5 5

Sample Output 2

598946612
479157290
463185380
682000542
771443236

Sample Input 3

10 6

Sample Output 3

0
166374059
207967574
610038216
177927813
630578223
902091444
412046453
481340945
404612686

见题面 Input 部分

见题面 Output 部分