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 Kotlin (1.0.0) (judge verdict: Accepted)

private fun readInts() = readLine()!!.split(" ").map(String::toInt)

private val MOD = 1000000007
private val NOT_YET = -1

fun main(args: Array<String>) {
    val (N, M) = readInts()
    val a = (0 until M).map { readLine()!!.toInt() - 1 } // 0-indexed

    if (N == 1) {
        println(1)
        return
    }

    val ways = Array(N) { NOT_YET }
    a.forEach { hole -> ways[hole] = 0 }

    if (ways[0] == NOT_YET) ways[0] = 1
    if (ways[1] == NOT_YET) ways[1] = 1 + ways[0]
  
    (2 until N)
        .filter { position -> ways[position] == NOT_YET }
        .asSequence()
        .forEach { ways[it] = (ways[it - 1] + ways[it - 2]) % MOD }

    println(ways.last())
}