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 (1.42.0) (judge verdict: Accepted)

fn solve() {
    let n: usize = read();
    let m = read();
    let mut a: HashSet<usize> = HashSet::new();
    for i in 0..m {
        a.insert(read::<usize>() - 1);
    }
    // -1, 0, 1, ... n
    let mut anss = vec![0; n + 2];
    anss[1] = 1;
    for i in 2..n + 2 {
        if !a.contains(&(i - 2)) {
            anss[i] = (anss[i - 1] + anss[i - 2]) % MOD;
        }
    }
    println!("{}", anss[n + 1]);
}

fn main() {
    let stack_size = 104_857_600;
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min, Reverse};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: usize = 1_000_000_007;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// =========