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)

fun main(args : Array<String>) {
    val (N, M) = readLine()!!.split(" ").map { it.toInt() }
    val a = mutableListOf<Int>()
    (1..M).forEach {
        val num = readLine()!!.toInt()
        a.add(num)
    }

    val dp = Array(N + 1, { 0L })
    dp[0] = 1
    val MOD = 1000000007

    var index = 0
    (1..N).forEach { n ->
        val isNthBroken = if (index >= M) false else a[index] == n
        if (isNthBroken) {
            index++
        }

        if (isNthBroken) {
            dp[n] = 0
        } else {
            if (n -2 >= 0) {
                dp[n] = (dp[n-1] + dp[n-2]) % MOD
            } else {
                dp[n] = dp[n-1]
            }
        }
    }
    println(dp[N])
}