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_imports)]

use std::cmp::{max, min, Ordering};
use std::collections::*;
#[cfg(debug_assertions)]
include! {"./debug.rs"}

#[cfg(not(debug_assertions))]
macro_rules! debug {
    ($($arg:expr),*) => {};
}

macro_rules! read {
    ([$t:ident] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ([$t:ident]) =>
        (rl().split_whitespace().map(|w| read_type!(w, $t)).collect::<Vec<_>>());
    (_, [$t:ident] ; $n:expr) =>
        ((0..$n).map(|_| read!(_, [$t])).collect::<Vec<_>>());
    (_, [$t:ident]) =>
        (rl().split_whitespace().skip(1).map(|w| read_type!(w, $t)).collect::<Vec<_>>());
    ($($t:ident),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ($t:ident) => (read_type!(rl(), $t));
    ($($t:ident),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(read_type!(w.next().unwrap(), $t)),*)
    }};
}

macro_rules! read_type {
    ($s:expr, chars) => {
        $s.chars().collect::<Vec<char>>()
    };
    ($s:expr, usize1) => {
        read_type!($s, usize) - 1
    };
    ($s:expr, $t:ty) => {
        $s.parse::<$t>().unwrap()
    };
}

fn rl() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_owned()
}

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}

////////////////////////////////////////////////////////////////////////////////

fn main() {
    let (n, m) = read!(usize, usize);
    let mut a = read!(i64; m);
    a.insert(0, -1);
    a.push((n + 1) as i64);
    debug!(a);

    let b = (0..m + 1).map(|i| a[i + 1] - a[i] - 1).vec();
    debug!(b);

    let mut ans: i64 = 1;
    for x in b {
        ans *= if x == 0 {
            0
        } else if x <= 1 {
            1
        } else {
            let x = x as usize;
            let mut s = vec![0; x];
            s[0] = 1;
            s[1] = 1;
            for i in 2..x {
                s[i] = (s[i - 2] + s[i - 1]) % 1_000_000_007;
            }
            s[x - 1]
        };
        ans %= 1_000_000_007;
    }

    println!("{}", ans);
}