Infinite Sequence

AtCoder

IDarc071_d

Time2000ms

Memory256MB

Difficulty—

How many infinite sequences $a_1, a_2, ...$ consisting of {${1, ... ,n}$} satisfy the following conditions? * The $n$\-th and subsequent elements are all equal. That is, if $n \leq i,j$, $a_i = a_j$. * For every integer $i$, the $a_i$ elements immediately following the $i$\-th element are all equal. That is, if $i < j < k\leq i+a_i$, $a_j = a_k$. Find the count modulo $10^9+7$. ## Constraints * $1 \leq n \leq 10^6$ ## Input Input is given from Standard Input in the following format: $n$ [samples]

Samples

Input #1

Output #1

4

The four sequences that satisfy the conditions are:

*   $1, 1, 1, ...$
*   $1, 2, 2, ...$
*   $2, 1, 1, ...$
*   $2, 2, 2, ...$

Input #2

Output #2

968545283

API Response (JSON)

{
  "problem": {
    "name": "Infinite Sequence",
    "description": {
      "content": "How many infinite sequences $a_1, a_2, ...$ consisting of {${1, ... ,n}$} satisfy the following conditions? *   The $n$\\-th and subsequent elements are all equal. That is, if $n \\leq i,j$, $a_i = a_j",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc071_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "How many infinite sequences $a_1, a_2, ...$ consisting of {${1, ... ,n}$} satisfy the following conditions?\n\n*   The $n$\\-th and subsequent elements are all equal. That is, if $n \\leq i,j$, $a_i = a_j...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments