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Contest: Task: Related: TaskG TaskI

Score : $600$ points

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 $k=i$.

Sample Input 1

4 2

Sample Output 1

1
2
1
0
  • For $k=1$, there is one multiset $A$ that satisfies the conditions: $\{4\}$.
  • For $k=2$, there are two multisets $A$ that satisfy the conditions: $\{1,3\}$ and $\{2,2\}$.
  • For $k=3$, there is one multiset $A$ that satisfies the conditions: $\{1,1,2\}$.
  • For $k=4$, there is no multiset $A$ that satisfies the conditions.

Sample Input 2

7 7

Sample Output 2

1
3
4
3
2
1
1