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.io.PrintWriter
import java.util.*

val pw = PrintWriter(System.out)
val DIVIDER: Long = (1e+9 + 7).toLong()
fun main(args: Array<String>) {
    val (n, m) = readListOfInt()
    val floors: MutableList<Long> = (0L..(n+1).toLong()).toMutableList()
    for(i in 0 until(n+1)) {
        floors[i] = 0L
    }
    for(i in 0 until m) {
        val a = readInt() 
        floors[a] = -1L
    }

    floors[1] = if(floors[1] == -1L) 0 else 1

    if(n > 1) {
        floors[2] = if(floors[2] == -1L) 0 else floors[1] + 1L
        for(i in 3 .. n) {
            if(floors[i] == -1L) {
                floors[i] = 0L
                continue
            } 
            val one_step = floors[i-1]
            val two_step = floors[i-2]
            floors[i] = (one_step + two_step) % DIVIDER
        }
    }
    println(floors[n] % DIVIDER)

    pw.flush()
}

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

fun sum_digits(num_: Long): Long {
    var num = num_
    var rtn: Long = 0
    while(num != 0.toLong()) {
        val tmp = num % 10
        rtn += tmp
        num /= 10
    }
    return rtn
}

/****** Decrared Functions ******/

// IO
fun read() = readLine()!!
fun readInt() = read().toInt()
fun readLong() = read().toLong()
fun readDouble() = read().toDouble()
fun readListOfString() = read().split(" ")
fun readListOfInt() = readListOfString().map { it.toInt() }
fun readListOfLong() = readListOfString().map { it.toLong() }
fun readListOfDouble() = readListOfString().map { it.toDouble() }


//fun println(value : Any) {
//    pw.println(value)
//}

fun gcd(a: Long, b: Long): Long = 
    if(b != 0L) a else gcd(b, a % b)

fun lcm(a: Long, b: Long) = 
    if(b==0L) a else gcd(b, a % b)