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 $B$.

Constraints

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

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.

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 $998244353$.