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)

const divider = 1e9+7;

var _fibs = [0, 1];
function fib(n) {
  for(var i = _fibs.length; i <= n; i++){
    _fibs[i] = (_fibs[i-1]%divider + _fibs[i-2]%divider)%divider;
  }
}

function fibs(n) {
  if(n<=0){return 1;}
  fib(n);
  return _fibs.slice(n, n + 1)[0];
}

function main(input){
  const lines = input.split('\n')
  const N_M = lines.shift().split(' ').map(x => parseInt(x));
  const N = N_M[0];
  const M = N_M[1];
  const A = []
  for(var i=0;i<M;i++){
    A.push(parseInt(lines.shift()));
  }

  if(M>1){
    for(var i=1;i<M;i++){
      if(A[i]-A[i-1]==1){
        console.log(0);
        return;
      }
    }
  }

  const diffs = [];
  A.unshift(-1);
  A.push(N+1);

  for(var i=1;i<M+2;i++){
    diffs.push(A[i]-A[i-1]-1)
  }

  var result = 1;

  for(diff of diffs){
//    console.log([result,diff,fibs(diff)]);
    result = (result * fibs(diff))%divider;
  }
  result = result%divider;

//  console.log(diffs);
  console.log(result);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));