Problem:
Score : 300 points

Problem Statement

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

Output

Print the number of ways to climb up the stairs under the condition, modulo 1\ 000\ 000\ 007.

Sample Input 1

6 1
3

Sample 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

Sample Input 2

10 2
4
5

Sample Output 2

0

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

Sample Input 3

100 5
1
23
45
67
89

Sample Output 3

608200469

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

Solution in Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn

object Main {

  def main(args: Array[String]) = {

    val Array(n, m) = StdIn.readLine().split(' ').map(_.toInt)
    val as: Set[Int] = (1 to m).foldLeft(Set(): Set[Int])((s, _) =>
      s + StdIn.readLine().toInt
    )

    println(solve(n, as))

  }

  def solve(n: Int, as: Set[Int]): Int = {

    val r = 1000000007
    def local(i: Int, prepre: Int, pre: Int): Int = {
      val now: Int = if (as.contains(i)) {
        0
      } else {
        (prepre + pre) % r
      }
      if (i == n) {
        now
      } else {
        local(i + 1, pre, now)
      }
    }

    local(1, 0, 1)
  }

}