Distance to Different
Description
Consider an array $a$ of $n$ integers, where every element is from $1$ to $k$, and every integer from $1$ to $k$ appears at least once.
Let the array $b$ be constructed as follows: for the $i$-th element of $a$, $b_i$ is the distance to the closest element in $a$ which is not equal to $a_i$. In other words, $b_i = \min \limits_{j \in [1, n], a_j \ne a_i} |i - j|$.
For example, if $a = [1, 1, 2, 3, 3, 3, 3, 1]$, then $b = [2, 1, 1, 1, 2, 2, 1, 1]$.
Calculate the number of different arrays $b$ you can obtain if you consider all possible arrays $a$, and print it modulo $998244353$.
The only line of the input contains two integers $n$ and $k$ ($2 \le n \le 2 \cdot 10^5$; $2 \le k \le \min(n, 10)$).
Print one integer — the number of different arrays $b$ you can obtain, taken modulo $998244353$.
Input
The only line of the input contains two integers $n$ and $k$ ($2 \le n \le 2 \cdot 10^5$; $2 \le k \le \min(n, 10)$).
Output
Print one integer — the number of different arrays $b$ you can obtain, taken modulo $998244353$.
2 2
4 3
6 2
6 5
133 7
1
3
20
3
336975971