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: Wrong Answer)

import java.util.Scanner;

fun main(args: Array<String>){
  val sc = Scanner(System.`in`)
  var N = sc.nextInt()
  var M = sc.nextInt()
  
  val limit = 1000000007
  var total = 1
  var nowBroken = -1
  var wasBroken = -1
  while(M > 0){
    nowBroken = sc.nextInt()
    total *= patternCount(nowBroken, wasBroken)
    if(total >= limit){
      total %= limit
    }
    wasBroken = nowBroken
    M--
  }
  total *= patternCount(N + 1, wasBroken)
  if(total >= limit){
    total %= limit
  }
  println(total)
}

private fun patternCount(now: Int, was: Int) :Int{
  var diff = now - was - 1
  when(diff){
    0 -> return 0
    else -> return fibonacci(1, 1, diff, 2)
  }
}

tailrec fun fibonacci( a: Int, b: Int, n: Int, c: Int) : Int =
	if(c >= n){
    	a
    }else{
      fibonacci( a + b, a, n, c + 1)
    }