{"raw_statement":[{"iden":"problem statement","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 $10^9+7$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq n \\leq 50$\n*   $0 \\leq k \\leq n^2$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$n$ $k$"},{"iden":"sample input 1","content":"3 2"},{"iden":"sample output 1","content":"2\n\nThere are six permutations of {$1,\\ 2,\\ 3$}. Among them, two have oddness of $2$: {$2,\\ 1,\\ 3$} and {$1,\\ 3,\\ 2$}."},{"iden":"sample input 2","content":"39 14"},{"iden":"sample output 2","content":"74764168"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}