Typical Stairs

AtCoder

IDabc129_c

Time2000ms

Memory256MB

Difficulty—

There is a staircase with $N$ steps. Takahashi is now standing at the foot of the stairs, that is, on the $0$\-th step. He can climb up one or two steps at a time. However, the treads of the $a_1$\-th, $a_2$\-th, $a_3$\-th, $\ldots$, $a_M$\-th steps are broken, so it is dangerous to set foot on those steps. How many are there to climb up to the top step, that is, the $N$\-th step, without setting foot on the broken steps? Find the count modulo $1\ 000\ 000\ 007$. ## Constraints * $1 \leq N \leq 10^5$ * $0 \leq M \leq N-1$ * $1 \leq a_1 < a_2 < $ $...$ $< a_M \leq N-1$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $a_2$ $ .$ $ .$ $ .$ $a_M$ [samples]

Samples

Input #1

6 1
3

Output #1

4

There are four ways to climb up the stairs, as follows:

*   $0 \to 1 \to 2 \to 4 \to 5 \to 6$
*   $0 \to 1 \to 2 \to 4 \to 6$
*   $0 \to 2 \to 4 \to 5 \to 6$
*   $0 \to 2 \to 4 \to 6$

Input #2

10 2
4
5

Output #2

0

There may be no way to climb up the stairs without setting foot on the broken steps.

Input #3

Output #3

608200469

Be sure to print the count modulo $1\ 000\ 000\ 007$.

API Response (JSON)

{
  "problem": {
    "name": "Typical Stairs",
    "description": {
      "content": "There is a staircase with $N$ steps. Takahashi is now standing at the foot of the stairs, that is, on the $0$\\-th step. He can climb up one or two steps at a time. However, the treads of the $a_1$\\-th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc129_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a staircase with $N$ steps. Takahashi is now standing at the foot of the stairs, that is, on the $0$\\-th step. He can climb up one or two steps at a time.\nHowever, the treads of the $a_1$\\-th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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