CF1051D.Bicolorings

You are given a grid, consisting of $2$ rows and $n$ columns. Each cell of this grid should be colored either black or white.

Two cells are considered neighbours if they have a common border and share the same color. Two cells $A$ and $B$ belong to the same component if they are neighbours, or if there is a neighbour of $A$ that belongs to the same component with $B$.

Let's call some bicoloring beautiful if it has exactly $k$ components.

Count the number of beautiful bicolorings. The number can be big enough, so print the answer modulo $998244353$.

给你一个由 $2$ 行 $n$ 列组成的网格。该网格的每个格子需被染成黑色或白色。

若两个格子拥有公共边且颜色相同，则称它们为相邻。若两个格子 $A$ 和 $B$ 相邻，或存在 $A$ 的某个相邻格子与 $B$ 属于同一连通块，则称 $A$ 和 $B$ 属于同一连通块。

若某种双色染色方案恰好形成 $k$ 个连通块，则称其为优美的（beautiful）。

请计算优美的双色染色方案总数。答案可能很大，请对 $998244353$ 取模后输出。

The only line contains two integers $n$ and $k$ ($1 \le n \le 1000$, $1 \le k \le 2n$) — the number of columns in a grid and the number of components required.

唯一一行包含两个整数 $n$ 和 $k$（$1 \le n \le 1000$，$1 \le k \le 2n$）—— 分别表示网格的列数和所需的连通块数量。

Print a single integer — the number of beautiful bicolorings modulo $998244353$.

输出一个整数——美丽双色染色方案的数量对 $998244353$ 取模的结果。

One of possible bicolorings in sample $1$:

样例 $1$ 中的一种可能的双色染色方案：