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 mod = 1000000007L
    val (n, m) = readLine()!!.split(' ').map(String::toLong)
    val aList = mutableListOf<Long>()
    if (m > 0L) {
        aList.add(readLine()!!.toLong())
    }
    (1 until m).forEach {
        val a = readLine()!!.toLong()
        if (aList.last() + 1 == a) {
            println(0)
            return
        }
        aList.add(a)
    }

    val dp = LongArray(n.toInt() + 1) { 0L }
    dp[0] = 1L
    aList.forEach { dp[it.toInt()] = -1L }

    for (i in 0..n.toInt() - 2) {
        if (dp[i] == -1L) continue
        if (dp[i + 1] != -1L) dp[i + 1] = (dp[i + 1] + dp[i]) % mod
        if (dp[i + 2] != -1L) dp[i + 2] = (dp[i + 2] + dp[i]) % mod
    }
    if (dp[n.toInt() - 1] != -1L) dp[n.toInt()] = (dp[n.toInt()] + dp[n.toInt() - 1]) % mod
    println(dp[n.toInt()])
}