{"raw_statement":[{"iden":"problem statement","content":"Find the number, modulo $998244353$, of permutations $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$ such that:\n\n*   $|P_i - i| \\ge X$ for all integers $i$ with $1 \\le i \\le N$."},{"iden":"constraints","content":"*   $1 \\le N \\le 100$\n*   $1 \\le X \\le 5$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $X$"},{"iden":"sample input 1","content":"3 1"},{"iden":"sample output 1","content":"2\n\nThe conforming permutations $P=(P_1,P_2,P_3)$ are the following two, $(2,3,1)$ and $(3,1,2)$, so the answer is $2$."},{"iden":"sample input 2","content":"5 2"},{"iden":"sample output 2","content":"4"},{"iden":"sample input 3","content":"98 5"},{"iden":"sample output 3","content":"809422418"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}