Bicolorings

**题目大意：** 给定一个$2\times n$的棋盘，可以对上面的格子黑白染色，求染色后棋盘上的联通块的个数正好为$k$的染色方案数 **输入格式：** 一行两个整数$n,k$ **输出格式：** 一个整数，表示方案数

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 $ .

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.

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

3 4

12

4 1

2

1 2

2

One of possible bicolorings in sample $ 1 $ :