{"problem":{"name":"Ban Permutation","description":{"content":"Find the number, modulo $998244353$, of permutations $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$ such that: *   $|P_i - i| \\ge X$ for all integers $i$ with $1 \\le i \\le N$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc309_g"},"statements":[{"statement_type":"Markdown","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 $1 \\le i \\le N$.\n\n## Constraints\n\n*   $1 \\le N \\le 100$\n*   $1 \\le X \\le 5$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $X$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc309_g","tags":[],"sample_group":[["3 1","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 $2$."],["5 2","4"],["98 5","809422418"]],"created_at":"2026-03-03 11:01:14"}}