CF1051D.Bicolorings

普及/提高-

通过率：0%

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题目描述

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 $998244353$ .

输入格式

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.

输出格式

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

输入输出样例

输入#1
```
3 4
```
输出#1
```
12
```
输入#2
```
4 1
```
输出#2
```
2
```
输入#3
```
1 2
```
输出#3
```
2
```

说明/提示

One of possible bicolorings in sample $1$ :

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