Problem Statement

You are given integers N and K such that $2\leq K\leq N$.

Problem: potato
We have a weighted rooted tree with N vertices numbered 1 to N. Vertex 1 is the root.
For each $2\leq i\leq N$, the parent of vertex i is p_{i}$;(1\leq p_{i}<i)$, and the edge connecting i and p_{i} has a weight of q_{i-1}.
Here, $q=(q_{1},q_{2},\dots,q_{N-1})$ is a permutation of $(1,2,\dots,N-1)$.
Let cost(u,v) be the maximum weight of an edge in the simple path connecting vertices u and v.
Find $\sum_{u=1}^{N} \sum_{v=u+1}^{N} cost(u,v)$.

Problem: tomato
You are given an integer a such that $1\leq a\lt K.$ There are $\frac{((N-1)$!)^{2}}{K-1} possible pairs of p and q in the problem "potato" such that p_{K}=a. Find the sum, modulo 998244353, of the answers to the problem over all those pairs.

For each $a=1,\dots,K-1,$ find the answer to the problem "tomato".

Input

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

Output

Print K-1 lines. The i-th line should contain the answer to the problem "tomato" for a=i.

Constraints

• $2\leq K\leq N\leq 10^{5}$
• All input values are integers.

Sample Input 1

4 4

Sample Output 1

170
170
172

Sample Input 2

3 2

Sample Output 2

20

Sample Input 3

16 7

Sample Output 3

457991130
457991130
65525944
418314090
644126049
676086428

见题面 Input 部分

见题面 Output 部分