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(arr:Array<String>) {
    val (totalStep, brokenCount) = readLine()!!.split(" ").map { it.toInt() }
    val broken = (1..brokenCount).map { readLine()!!.toInt() }.toMutableList()
    broken.add(totalStep  + 1)
    setDic(totalStep+1)
    var current = 0
    var ans = 1L
    for (step in broken) {
        if(current >= step) {
            println(0)
            return
        }
        if(step - current == 1) {
            current = step + 1
            continue
        }
        ans *= dic[step - current - 1]
        ans %= md
        current = step + 1
    }
    println(ans)
}

val md = 1000000000 + 7

val dic = mutableListOf(0L, 1L, 2L)
fun setDic(num:Int) {
    for(i in 3..num) {
        val tmp = (dic[i-2] + dic[i-1]) % md
        dic.add(tmp)
    }
}