Candy Retribution

AtCoder

IDjsc2019_qual_f

Time2000ms

Memory256MB

Difficulty—

Find the number of sequences of $N$ non-negative integers $A_1, A_2, ..., A_N$ that satisfy the following conditions: * $L \leq A_1 + A_2 + ... + A_N \leq R$ * When the $N$ elements are sorted in non-increasing order, the $M$\-th and $(M+1)$\-th elements are equal. Since the answer can be enormous, print it modulo $10^9+7$. ## Constraints * All values in input are integers. * $1 \leq M < N \leq 3 \times 10^5$ * $1 \leq L \leq R \leq 3 \times 10^5$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $L$ $R$ [samples]

Samples

Input #1

4 2 3 7

Output #1

105

The sequences of non-negative integers that satisfy the conditions are:
$\begin{aligned} &(1, 1, 1, 0), (1, 1, 1, 1), (2, 1, 1, 0), (2, 1, 1, 1), (2, 2, 2, 0), (2, 2, 2, 1), \\ &(3, 0, 0, 0), (3, 1, 1, 0), (3, 1, 1, 1), (3, 2, 2, 0), (4, 0, 0, 0), (4, 1, 1, 0), \\ &(4, 1, 1, 1), (5, 0, 0, 0), (5, 1, 1, 0), (6, 0, 0, 0), (7, 0, 0, 0)\end{aligned}$
and their permutations, for a total of $105$ sequences.

Input #2

2 1 4 8

Output #2

3

The three sequences that satisfy the conditions are $(2, 2)$, $(3, 3)$, and $(4, 4)$.

Input #3

141592 6535 89793 238462

Output #3

933832916

API Response (JSON)

{
  "problem": {
    "name": "Candy Retribution",
    "description": {
      "content": "Find the number of sequences of $N$ non-negative integers $A_1, A_2, ..., A_N$ that satisfy the following conditions: *   $L \\leq A_1 + A_2 + ... + A_N \\leq R$ *   When the $N$ elements are sorted in",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "jsc2019_qual_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Find the number of sequences of $N$ non-negative integers $A_1, A_2, ..., A_N$ that satisfy the following conditions:\n\n*   $L \\leq A_1 + A_2 + ... + A_N \\leq R$\n*   When the $N$ elements are sorted in...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments