Division into Two

AtCoder

IDagc009_c

Time2000ms

Memory256MB

Difficulty—

There is a set consisting of $N$ distinct integers. The $i$\-th smallest element in this set is $S_i$. We want to divide this set into two sets, $X$ and $Y$, such that: * The absolute difference of any two distinct elements in $X$ is $A$ or greater. * The absolute difference of any two distinct elements in $Y$ is $B$ or greater. How many ways are there to perform such division, modulo $10^9 + 7$? Note that one of $X$ and $Y$ may be empty. ## Constraints * All input values are integers. * $1 ≦ N ≦ 10^5$ * $1 ≦ A , B ≦ 10^{18}$ * $0 ≦ S_i ≦ 10^{18}(1 ≦ i ≦ N)$ * $S_i < S_{i+1}(1 ≦ i ≦ N - 1)$ ## Input The input is given from Standard Input in the following format: $N$ $A$ $B$ $S_1$ : $S_N$ [samples]

Samples

Input #1

Output #1

5

There are five ways to perform division:

*   $X=${$1,6,9,12$}, $Y=${$3$}
*   $X=${$1,6,9$}, $Y=${$3,12$}
*   $X=${$3,6,9,12$}, $Y=${$1$}
*   $X=${$3,6,9$}, $Y=${$1,12$}
*   $X=${$3,6,12$}, $Y=${$1,9$}

Input #2

Output #2

Input #3

Output #3

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Division into Two",
    "description": {
      "content": "There is a set consisting of $N$ distinct integers. The $i$\\-th smallest element in this set is $S_i$. We want to divide this set into two sets, $X$ and $Y$, such that: *   The absolute difference of",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc009_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a set consisting of $N$ distinct integers. The $i$\\-th smallest element in this set is $S_i$. We want to divide this set into two sets, $X$ and $Y$, such that:\n\n*   The absolute difference of...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments