A12134. 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 $998244353$ .

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 $998244353$ .

One of possible bicolorings in sample $1$ :