Problem Statement

You are given positive integers $N$ and $K$ satisfying $1\leq K\leq N$.

For a permutation $P = (P_{1}, P_{2}, \dots , P_{N})$ of $(1, 2, \dots , N)$, define $f(P)$ as follows:

• The minimum possible value of the number of inversions of a length-$N$ integer sequence $A = (A_{1}, A_{2}, \dots, A_{N})$ satisfying the following condition:
• $|A_{i}| = P_{i}$ for every integer $1\leq i\leq N$.

For $a = 1, 2, \dots, N$, answer the following question:

There are $(N - 1)!$ permutations $P = (P_{1}, P_{2}, \dots , P_{N})$ of $(1, 2, \dots , N)$ satisfying $P_{K} = a$. Find the sum, modulo $998244353$, of $f(P)$ over all of them.

Constraints

• $1\leq K\leq N\leq 2\times 10^{5}$
• All input values are integers.

Input

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

N K

Output

Output $N$ lines. The $i$-th line should contain the answer for $a = i$.