Problem Statement

Given are positive integers $N$ and $M$.

For each $k=1,2,\ldots,N$, find the following number and print it modulo $998244353$.

• The number of multisets $A$ containing $k$ positive integers that satisfy both of the following conditions:
• the sum of the elements of $A$ is $N$;
  • for every positive integer $x$, $A$ contains at most $M$ occurrences of $x$.

Constraints

• $1 \leq M \leq N \leq 5000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print $N$ lines; the $i$-th line $(1 \leq i \leq N)$ should contain the answer for the case $k=i$.