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 12.16.1) (judge verdict: Accepted)

function spilitInput(input, to_int) {
  if (typeof to_int === 'undefined') to_int = false;
  var splited = [];
  var rows = input.split('\n');
  for (var i = 0; i < rows.length; i += 1) {
    if (to_int) {
      splited.push(rows[i].split(' ').map(function(d){return parseInt(d,10);}));
    } else {
      splited.push(rows[i].split(' '));
    }
  }
  return splited;
}

function initDp(N, init_n) { return Array(N+2).fill(init_n); }
function chmin(a, b) { if (a > b) a = b; }
function chmax(a, b) { if (a < b) a = b; }

function Main(input) {
  var splited = spilitInput(input, true);
  var N = splited[0][0];
  var hasons = [];
  for (var i = 1; i < splited.length; i += 1) {
    hasons.push(splited[i][0]);
  }
    
  var dp = initDp(N, 0);
  dp[0] = 1;
  
  for (var i = 1; i <= N; i += 1) {
    if (hasons[0] == i) {
      hasons.shift();
      continue;
    }
    dp[i] += dp[i - 1];
    if (i >= 2) dp[i] += dp[i - 2];
    dp[i] %= 1000000007;
  }

  console.log(dp[N]);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));