{"raw_statement":[{"iden":"problem statement","content":"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 $X$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 3000$\n*   $1 \\leq X \\leq 2N$\n*   $N$ and $X$ are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $X$"},{"iden":"sample input 1","content":"3 3"},{"iden":"sample output 1","content":"14\n\n$14$ 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 $(2,2,2)$."},{"iden":"sample input 2","content":"8 6"},{"iden":"sample output 2","content":"1179"},{"iden":"sample input 3","content":"10 1"},{"iden":"sample output 3","content":"1024"},{"iden":"sample input 4","content":"9 13"},{"iden":"sample output 4","content":"18402"},{"iden":"sample input 5","content":"314 159"},{"iden":"sample output 5","content":"459765451"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}