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)

macro_rules! get {
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
                    get!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
                    get!($($t),*)
        ).collect::<Vec<_>>()
    };
    ($t:ty |) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.split_whitespace()
                .map(|t| t.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
    ($t:ty | $n:expr) => {
        (0..$n).map(|_| get!($t |)).collect::<Vec<_>>()
    };
}

const MOD: u64 = 1_000_000_007;

fn fac(n: u64) -> u64 {
    if n <= 1 {
        return 1;
    } else {
        return n * fac(n - 1);
    }
}

fn count(steps: u64) -> u64 {
    let max_twos = steps >> 1;
    if steps == 0 {
        return 1;
    }
    let mut cnt = 0;
    for twos in 0..(max_twos+1) {
        let ones = steps - twos * 2;
        cnt += (fac(twos + ones) / (fac(twos) * fac(ones))) % MOD;
    }
    cnt % MOD
}

fn main() {
    let (N, M) = get!(u64, u64);
    let mut As = get!(u64; M);
    As.sort();
    let mut cnt = 1;
    let mut pos = 0;
    let mut prev_a = 0;
    for i in 0..As.len() {
        let a = As[i];
        if a == pos || (a == prev_a + 1 && i > 0) {
            println!("0");
            return;
        }
        cnt *= count((a - 1) - pos);
        cnt = cnt % MOD;
        prev_a = a;
        pos = a + 1;
    }
    cnt *= count(N - pos);
    cnt = cnt % MOD;
    println!("{}", cnt);
}