Problem Statement

You are given positive integers $N$ and $M$. For each $k=1,\ldots,N$, solve the following problem.

• Problem: We will divide $N$ people with ID numbers $1$ through $N$ into $k$ non-empty groups. Here, people whose ID numbers are equal modulo $M$ cannot belong to the same group. How many such ways are there to divide people into groups? Since the answer may be enormous, find it modulo $998244353$.

Here, two ways to divide people into groups are considered different when there is a pair $(x, y)$ such that Person $x$ and Person $y$ belong to the same group in one way but not in the other.

Constraints

• $2 \leq N \leq 5000$
• $2 \leq M \leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print $N$ lines.

The $i$-th line should contain the answer for the problem with $k=i$.