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)

#![allow(unused_mut, unused_macros, unused_variables, unused_assignments, non_snake_case)]

macro_rules! get {
    ($($s:tt : $t:ty),*) => {
        let stdin = std::io::stdin();
        let mut buf = String::new();
        stdin.read_line(&mut buf).unwrap();
        let mut iter = buf.split_whitespace();
        $(let $s:$t = iter.next().unwrap().parse().unwrap();)*
    };
}

macro_rules! get_v {
    ($s:tt : $t:ty) => {
        let stdin = std::io::stdin();
        let mut buf = String::new();
        stdin.read_line(&mut buf).unwrap();
        let iter = buf.split_whitespace();
        let $s:Vec<$t> = iter.map(|x| x.parse::<$t>().unwrap()).collect();
    };
}

macro_rules! get_vv {
    ($s:tt[$n:tt] : $t:ty) => {
        let mut t:Vec<$t> = Vec::new();

        let stdin = std::io::stdin();
        for _ in 0..$n {
            let mut buf = String::new();
            stdin.read_line(&mut buf).unwrap();
            t.push(buf.trim().parse().unwrap());
            //get_v!{a:usize}
            //t.push(a);
        }
        let $s = t;
    };
}


fn main() {
    get! {
        N : usize,
        M : usize
    }
    get_vv! {
        A[M]: usize
    }
    let MOD = 1_000_000_007;
    let mut steps = vec!(0; N + 1);
    for a in A {
        steps[a] = -1;
    }
    steps[0] = 1;
    for n in 1..N + 1 {
        if -1 == steps[n] {continue;}
        if -1 == steps[n - 1] && -1 == steps[n - 2] {
            println!("0");
            return;
        }
        if -1 != steps[n - 1] {
            steps[n] += steps[n - 1] % MOD;
        }
        if 1 < n && -1 != steps[n - 2] {
            steps[n] += steps[n - 2] % MOD;
        }
    }
    println!("{:?}", steps[N] % MOD);
}