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.

Sample Input 1

3 3

Sample Output 1

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).

Sample Input 2

8 6

Sample Output 2

1179

Sample Input 3

10 1

Sample Output 3

1024

Sample Input 4

9 13

Sample Output 4

18402

Sample Input 5

314 159

Sample Output 5

459765451