Problem Statement

Given positive integers $N,K$ and $M$, solve the following problem for every integer $x$ between $1$ and $N$ (inclusive):

• Find the number, modulo $M$, of non-empty multisets containing between $0$ and $K$ (inclusive) instances of each of the integers $1,2,3\cdots ,N$ such that the average of the elements is $x$.

Constraints

• $1\le N,K\le 100$
• 108≤M≤109+9
• $M$ is prime.
• All values in input are integers.

Sample Input 1

3 1 998244353

Sample Output 1

1
3
1

Consider non-empty multisets containing between $0$ and $1$ instance(s) of each of the integers between $1$ and $3$. Among them, there are:

• one multiset such that the average of the elements is $k=1$: $\{1\}$;
• three multisets such that the average of the elements is $k=2$: $\{2\},\{1,3\},\{1,2,3\}$;
• one multiset such that the average of the elements is $k=3$: $\{3\}$.

Sample Input 2

1 2 1000000007

Sample Output 2

2

Consider non-empty multisets containing between $0$ and $2$ instances of each of the integers between $1$ and $1$. Among them, there are:

• two multisets such that the average of the elements is $k=1$: $\{1\},\{1,1\}$.

Sample Input 3

10 8 861271909

Sample Output 3

8
602
81827
4054238
41331779
41331779
4054238
81827
602
8