Range Set

AtCoder

IDagc045_c

Time2000ms

Memory256MB

Difficulty—

Snuke has a string $x$ of length $N$. Initially, every character in $x$ is `0`. Snuke can do the following two operations any number of times in any order: * Choose $A$ consecutive characters in $x$ and replace each of them with `0`. * Choose $B$ consecutive characters in $x$ and replace each of them with `1`. Find the number of different strings that $x$ can be after Snuke finishes doing operations. This count can be enormous, so compute it modulo $(10^9+7)$. ## Constraints * $1 \leq N \leq 5000$ * $1 \leq A,B \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A$ $B$ [samples]

Samples

Input #1

4 2 3

Output #1

11

For example, $x$ can be `0011` or `1111` in the end, but cannot be `0110`.

Input #2

10 7 2

Output #2

Input #3

1000 100 10

Output #3

828178524

API Response (JSON)

{
  "problem": {
    "name": "Range Set",
    "description": {
      "content": "Snuke has a string $x$ of length $N$. Initially, every character in $x$ is `0`. Snuke can do the following two operations any number of times in any order: *   Choose $A$ consecutive characters in $x",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc045_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has a string $x$ of length $N$. Initially, every character in $x$ is `0`.\nSnuke can do the following two operations any number of times in any order:\n\n*   Choose $A$ consecutive characters in $x...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments