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: Accepted)

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
  let mut b = String::new();
  std::io::stdin().read_line(&mut b).ok();
  b.split_whitespace()
    .map(|x| x.parse().ok().unwrap())
    .collect()
}

fn main() {
  let v: Vec<usize> = read_vec();
  let (n, m) = (v[0], v[1]);

  let mut stairs: Vec<usize> = vec![1; n + 1];
  for _ in 0..m {
    let i: usize = read_vec()[0];
    stairs[i] = 0;
  }

  for i in 2..n + 1 {
    stairs[i] = stairs[i] * (stairs[i - 2] + stairs[i - 1]) % 1_000_000_007;
  }
  println!("{}", stairs[n]);
}