Bicolorings

2000ms

262144K

Description:

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 $$$998244353$$$.

Input:

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.

Output:

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

Sample Input:

3 4

Sample Output:

Sample Input:

4 1

Sample Output:

Sample Input:

1 2

Sample Output:

Note:

One of possible bicolorings in sample $$$1$$$:

$\text{[math]}$

Informação

Provedor Codeforces

Código CF1051D