Problem Description

After the release of NEKOPARA Vol.3, Azuki, who is not the main character in the new installment, finally gets some rest. To pass the time, she starts coloring a sequence consisting of $n$ squares, each of which can be painted in one of three colors: black, white, or gray. For aesthetic reasons, Azuki wants to ensure that no two black squares are adjacent and no two white squares are adjacent. There are many such sequences, and Azuki defines the weight of each sequence as the number of occurrences where a black square and a white square are adjacent, such as the sequence "gray black white black" having a weight of $2$. Azuki wants to know, for each $i$ satisfying $0 \le i \le k$, how many sequences of length $n$ with a weight of $i$ exist. Since the answers can be very large, she only needs to know the values modulo $998244353$. Azuki promises that if you solve this problem, she will make you a delicious cake.

Input Format

A single line containing two positive integers $n$ and $k$.

Output Format

A single line containing $k+1$ positive integers, representing the number of sequences with weights $0, 1, \dots, k$ modulo $998244353$.

Sample Input and Output

Sample Input #1

3 3

Sample Output #1

11 4 2 0

Sample Input #2

20 10

Sample Output #2

1398101 4582670 8103780 10126770 9931780 8075094 5618340 3422330 1841460 893790 383524

Notes/Hints

For $30\%$ of the test cases, $n, k \le 100$.

For $50\%$ of the test cases, $n, k \le 5000$ with a time limit of $1$ second. The remaining test cases have a time limit of $5$ seconds.

For $70\%$ of the test cases, $n, k \le 60000$.

For $100\%$ of the test cases, $n \le 10^{18}, k \le 100000$.

见题面 Input 部分

见题面 Output 部分