Enormous Atcoder Railroad

AtCoder

IDs8pc_4_e

Time1000ms

Memory256MB

Difficulty—

There is a railroad company in Atcoder Kingdom, "Atcoder Railroad". There are $N + 1$ stations numbered $0, 1, 2, ..., N$ along a railway. Currently, two kinds of train are operated, local and express. A local train stops at every station, and it takes one minute from station $i$ to $i + 1$, and vice versa. An express train only stops at station $S_0, S_1, S_2, ..., S_{K-1} (0 = S_0 < S_1 < S_2 < ... < S_{K-1} = N)$. It takes one minute from station $S_i$ to $S_{i + 1}$, and vice versa. But the president of Atcoder Railroad, Semiexp said it is not very convenient so he planned to operate one more kind of train, "semi-express". The stations where the semi-express stops (This is $T_0, T_1, T_2, ..., T_{L-1}$, $0 = T_0 < T_1 < T_2 < ... < T_{L-1} = N$) have to follow following conditions: From station $T_i$ to $T_{i+1}$ takes 1 minutes, and vice versa. * The center of Atcoder Kingdom is station $0$, and you have to be able to go to station $i$ atmost $X$ minutes. * If the express stops at the station, semi-express should stops at the station. Print the number of ways of the set of the station where semi-express stops (sequence $T$). Since the answer can be large, print the number modulo $10^9 + 7$. ## Input Format $N$ $K$ $X$ $S_0$ $S_1$ $S_2$ ... $S_{K-1}$ [samples]

API Response (JSON)

{
  "problem": {
    "name": "Enormous Atcoder Railroad",
    "description": {
      "content": "There is a railroad company in Atcoder Kingdom, \"Atcoder Railroad\".   There are $N + 1$ stations numbered $0, 1, 2, ..., N$ along a railway.   Currently, two kinds of train are operated, local and exp",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "s8pc_4_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a railroad company in Atcoder Kingdom, \"Atcoder Railroad\".  \nThere are $N + 1$ stations numbered $0, 1, 2, ..., N$ along a railway.  \nCurrently, two kinds of train are operated, local and exp...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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