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.

Input

Input is given from Standard Input in the following format:
N K M

Output

Use the following format:
c_1
c_2
:
c_N

Here, c_x should be the number, modulo M, of multisets such that the average of the elements is x.

Constraints

• $1 \leq N, K \leq 100$
• $10^8 \leq M \leq 10^9 + 9$
• 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

见题面 Input 部分

见题面 Output 部分