Problem Description

Given positive integers $ N $ and $ A $.

Let $ m $ be a positive integer. Sai has $ m $ special dice numbered from $ 1 $ to $ m $. Sai will roll each die $ A $ times. Each roll of die $ i $ ($1 \le i \le m$) has a probability of $\frac{1}{i^2}$ of landing on a "hit". These trials are all independent events.

What is the probability of getting exactly $ N $ hits in total? This value depends on $ m $, but we want to find the limit of this probability as $ m $ approaches infinity.

Let this limit be $ p $. It can be proven that there exist unique rational numbers $c_0, \ldots, c_{N-1}$ such that $p = \sum_{j=0}^{N-1} c_j \pi^j$ (where $\pi$ is the mathematical constant pi). Output these $c_0, \ldots, c_{N-1}$ modulo $ 998244353 $.

When outputting a rational number modulo $ 998244353 $, represent it as an irreducible fraction $\frac{x}{y}$. Output the integer $ z $ in the range $ 0 $ to $ 998244353 - 1 $ such that $ x - yz $ is divisible by $ 998244353 $. Due to the constraints of this problem, the value to be output is uniquely determined.

Input Format

The input is given from the standard input in the following format:

$ N $ $ A $

Output Format

Output $c_0, \ldots, c_{N-1}$ in this order, separated by spaces, modulo $ 998244353 $.

Sample Input and Output

Sample Input #1

1 1

Sample Output #1

499122177

Sample Input #2

2 1

Sample Output #2

623902721 0

Sample Input #3

3 1

Sample Output #3

686292993 0 353544875

Sample Input #4

3 2

Sample Output #4

623902721 0 0

Sample Input #5

10 5

Sample Output #5

748591874 0 809083222 0 440705764 0 0 0 0 0

Notes/Hints

Constraints

• $1 \le A \le N \le 250,000$.

Partial Points

• Correct answer for a dataset where $N \le 100$ and $ A = 1 $ will award $ 10 $ points.
• Correct answer for a dataset where $ A = 1 $ will award an additional $ 10 $ points.
• Correct answer for the dataset without additional constraints will award an additional $ 80 $ points.

Sample Explanation 1

$p = \frac{1}{2}$.

Sample Explanation 2

$p = \frac{3}{8}$.

Sample Explanation 3

$p = \frac{5}{16} - \frac{1}{48} \pi^2$.

Sample Explanation 4

$p = \frac{3}{8}$.

见题面 Input 部分

见题面 Output 部分