Redistribution

AtCoder

IDabc178_d

Time2000ms

Memory256MB

Difficulty—

Given is an integer $S$. Find how many sequences there are whose terms are all integers greater than or equal to $3$, and whose sum is equal to $S$. The answer can be very large, so output it modulo $10^9 + 7$. ## Constraints * $1 \leq S \leq 2000$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $S$ [samples]

Samples

Input #1

Output #1

3

$3$ sequences satisfy the condition: ${3,4}$, ${4,3}$ and ${7}$.

Input #2

Output #2

0

There are no sequences that satisfy the condition.

Input #3

Output #3

294867501

API Response (JSON)

{
  "problem": {
    "name": "Redistribution",
    "description": {
      "content": "Given is an integer $S$. Find how many sequences there are whose terms are all integers greater than or equal to $3$, and whose sum is equal to $S$. The answer can be very large, so output it modulo $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc178_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is an integer $S$. Find how many sequences there are whose terms are all integers greater than or equal to $3$, and whose sum is equal to $S$. The answer can be very large, so output it modulo $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments