Problem Statement

Find the number, modulo 998244353, of $non-decreasing sequences A=(A_1,A_2,\ldots,A_N)$ of length N consisting of integers between 0 and M (inclusive) that satisfy the following, for each $K=0,1,\ldots,\mathrm{MOD}-1$:

• the sum of the elements in A is congruent to $K modulo \mathrm{MOD}$.

What is a non-decreasing sequence?
A sequence B is non-decreasing if and only if $B_i \leq B_{i+1}$ for every integer $(1 \le i \le |B| - 1)$, where |B| is the length of B.

Input

Input is given from Standard Input in the following format:
$N M \mathrm{MOD}$

Output

For each $K=0,1,\ldots,\mathrm{MOD}-1$, print the number, modulo 998244353, of sequences that satisfy the condition.

Constraints

• $1 \leq N ,M\leq 10^6$
• $1\leq \mathrm{MOD}\leq 500$
• All values in input are integers.

Sample Input 1

2 2 4

Sample Output 1

2 1 2 1

There are 6 non-decreasing sequences of length 2 consisting of integers between 0 and 2: (0, 0), (0, 1),(0,2), (1,1),(1,2),(2,2). Here, we have:

• 2 sequences whose sums are congruent to 0 modulo 4: (0,0),(2,2);

• 1 sequence whose sum is congruent to 1 modulo 4: (0,1);

• 2 sequences whose sums are congruent to 2 modulo 4: (0,2),(1,1);

• 1 sequence whose sum is congruent to 3 modulo 4: (1,2).

Sample Input 2

3 45 3

Sample Output 2

5776 5760 5760

Sample Input 3

1000000 1000000 6

Sample Output 3

340418986 783857865 191848859 783857865 340418986 635287738

Print the counts modulo 998244353.

见题面 Input 部分

见题面 Output 部分