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)

import java.util.*
import java.math.*

fun main(args: Array<String>) {

    var (N, M) = readLine()!!.split(" ").map { it.toInt() }
//    var N = readLine()!!.toInt()
//    val D = readLine()!!.split(" ").map { it.toLong() }
//    val A = readLine()!!.split(" ").map { it.toInt() }.toIntArray()

    val mod = 1000000007L
    val dp = LongArray(N+1)
    var a = if (M--  > 0) readLine()!!.toInt() else 0
    dp[0] = 1
    dp[1] = if (a == 1) {if (M-- > 0) a = readLine()!!.toInt();0} else 1

    if ( N == 1) {
        println(dp[N])
        return
    }

    for (n in 2 .. N) {
        if (n == a) {
            if (M-- > 0)
                a = readLine()!!.toInt()
            continue
        }
        dp[n] = (dp[n-1] + dp[n-2]) % mod
    }

    println(dp[N])

//    println("%.9f".format(ans))
}