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) {
  input = input.trim().split('\n')
  const NM = input.shift().split(' ').map(v => Number(v))
  input = [0, ...input.map(v => Number(v)), NM[0]]
  console.log(input)

  const calc = d => {
    return d < 2 ? 1 : (d - 1) * (d - 2) / 2 + 2
  }
  let ans = 1
  
  for (let m = 1; m <= NM[1] + 1; m++) {
    let diff = input[m] - input[m - 1] - 1
    console.log(m, diff, calc(diff))
    if (diff === 0 && m!==1) {
      console.log(0)
      return
    }
    ans = ans * (calc(diff))
  }
  console.log(ans % 1000000007)
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));