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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分