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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

'use strict'

function Main(input) {
  const N = Number(input.split("\n")[0].split(" ")[0])
  const M = Number(input.split("\n")[0].split(" ")[1])
  const a = input.split("\n").slice(1).map(x => Number(x))
  
  if (M === 0) {
    console.log(fib(N))
    return
  }

  if (M > 1) {
    for (let i=1; i<M; i++) {
        if(a[i] - a[i-1] === 1) {
            console.log(0)
            return
        } 
    }
  }
  
  const list = []
  for(let i=0; i<=M; i++) {
    if(i === 0) {
        list.push(a[i] - 1)
        continue
    }
    if(i === M) {
        list.push(N - a[i-1] - 1)
        continue
    }
    list.push(a[i] - a[i-1] - 2)
  }

  let ans = 1
  for(let i=0; i<M+1; i++) {
      ans = (ans * fib(list[i])) % 1000000007
  }
  console.log(ans)
}

Main(require("fs").readFileSync("/dev/stdin", "utf8").trim())

function fib(x) {
    if(x === 1 || x === 0) {
        return 1
    }
    if(x === 2) {
        return 2
    }
    let last = 2
    let second = 1
    for(let i=3; i<=x; i++) {
        let total = (last + second) % 1000000007
        second = last
        last = total
    }
    return last
}