Score : $800$ points

Problem Statement

Find the number, modulo $998244353$, of sequences of length $N$ consisting of $0$, $1$ and $2$ such that none of their contiguous subsequences totals to $X$.

Constraints

• $1 \leq N \leq 3000$
• $1 \leq X \leq 2N$
• $N$ and $X$ are integers.

Input

Input is given from Standard Input in the following format:

$N$ $X$

Output

Print the number, modulo $998244353$, of sequences that satisfy the condition.

3 3

14

$14$ sequences satisfy the condition: $(0,0,0),(0,0,1),(0,0,2),(0,1,0),(0,1,1),(0,2,0),(0,2,2),(1,0,0),(1,0,1),(1,1,0),(2,0,0),(2,0,2),(2,2,0)$ and $(2,2,2)$.

8 6

1179

10 1

1024

9 13

18402

314 159

459765451