Problem Statement

Find the number of permutations $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$ that satisfy the following, modulo 998244353, for each $K=0,1,2,\dots,N-1$.

• There are exactly K integers i such that $1 \le i \le N-1$ and |P_i - P_{i+1}|=M.

Input

Input is given from Standard Input in the following format:
N M

Output

Print the number of permutations that satisfy the condition, modulo 998244353, for each $K=0,1,2,\dots,N-1$.

Constraints

• $2 \le N \le 250000$
• $1 \le M \le N-1$
• All values in input are integers.

Sample Input 1

3 1

Sample Output 1

0 4 2

• For K=0, the condition is satisfied by no permutations P.
• For K=1, the condition is satisfied by four permutations P: (1,3,2),(2,1,3),(2,3,1),(3,1,2).
• For K=2, the condition is satisfied by two permutations P: (1,2,3),(3,2,1).

Sample Input 2

4 3

Sample Output 2

12 12 0 0

Sample Input 3

10 5

Sample Output 3

1263360 1401600 710400 211200 38400 3840 0 0 0 0

见题面 Input 部分

见题面 Output 部分