{"problem":{"name":"Permutation Oddness","description":{"content":"Let us define the _oddness_ of a permutation $p$ = {$p_1,\\ p_2,\\ ...,\\ p_n$} of {$1,\\ 2,\\ ...,\\ n$} as $\\sum_{i = 1}^n |i - p_i|$. Find the number of permutations of {$1,\\ 2,\\ ...,\\ n$} of oddness $k$","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc134_f"},"statements":[{"statement_type":"Markdown","content":"Let us define the _oddness_ of a permutation $p$ = {$p_1,\\ p_2,\\ ...,\\ p_n$} of {$1,\\ 2,\\ ...,\\ n$} as $\\sum_{i = 1}^n |i - p_i|$.\nFind the number of permutations of {$1,\\ 2,\\ ...,\\ n$} of oddness $k$, modulo $10^9+7$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq n \\leq 50$\n*   $0 \\leq k \\leq n^2$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$n$ $k$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc134_f","tags":[],"sample_group":[["3 2","2\n\nThere are six permutations of {$1,\\ 2,\\ 3$}. Among them, two have oddness of $2$: {$2,\\ 1,\\ 3$} and {$1,\\ 3,\\ 2$}."],["39 14","74764168"]],"created_at":"2026-03-03 11:01:14"}}