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 $|P_i - P_{i+1}|=M$.

Constraints

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

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 $K=0,1,2,\\dots,N-1$.

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