Permutation Oddness

AtCoder

IDabc134_f

Time2000ms

Memory256MB

Difficulty—

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 $k$, modulo $10^9+7$. ## Constraints * All values in input are integers. * $1 \leq n \leq 50$ * $0 \leq k \leq n^2$ ## Input Input is given from Standard Input in the following format: $n$ $k$ [samples]

Samples

Input #1

3 2

Output #1

2

There are six permutations of {$1,\ 2,\ 3$}. Among them, two have oddness of $2$: {$2,\ 1,\ 3$} and {$1,\ 3,\ 2$}.

Input #2

39 14

Output #2

74764168

API Response (JSON)

{
  "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 $k$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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