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 Rust (1.15.1) (judge verdict: Runtime Error)

fn read() -> String {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf
}

fn main() {
  let v: Vec<usize> = read()
    .split_whitespace()
    .map(|x| x.parse().unwrap())
    .collect();
  let (n, m) = (v[0], v[1]);
  let a: Vec<usize> = (0..m).map(|_| read().trim().parse().unwrap()).collect();

  let mut stairs = vec![1_usize; n + 1];
  if a[0] == 1 {
    stairs[1] = 0;
  }
  for i in 2..n + 1 {
    stairs[i] = if a.contains(&i) {
      0
    } else {
      stairs[i - 2] + stairs[i - 1]
    }
  }
  println!("{}", stairs[n] % 1_000_000_007);
}