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 $x$.

Input is given from Standard Input in the following format:

```
$N$ $M$
```

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

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

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.