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::collections::HashMap;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

const MOD : usize = 1000_000_007;

fn main() {
    let nm = read_vec::<usize>();
    let n = nm[0];
    let m = nm[1];
    let mut amap = HashMap::new();
    let mut prev = 0;
    for _i in 0..m {
        let ai = read::<usize>();
        if ai <= prev {
            println!("0");
            return;
        }
        let key = ai - 1 - prev;
        let count = amap.entry(key).or_insert(0);
        *count += 1;
        prev = ai + 1;
    }
    let key = n - prev;
    {
        /* atcoderのRustだと中括弧でスコープを新しくつくらないと以下のようなエラーになる。
            error[E0502]: cannot borrow `amap` as mutable because it is also borrowed as immutable
            --> ./Main.rs:42:9
            |
         41 |         let current = amap.get(&key).unwrap();
            |                       ---- immutable borrow occurs here
         42 |         amap.insert(key, current + 1);
            |         ^^^^ mutable borrow occurs here
         43 | 
         44 |     } else {
            |     - immutable borrow ends here

            error: aborting due to previous error
        */
        let count = amap.entry(key).or_insert(0);
        *count += 1;
    }
    let answer = solve(n, &mut amap);
    println!("{}", answer);
}

fn solve(n: usize, aset:&mut HashMap<usize, i32>) -> usize {
    if n <= 1 {
        return 1;
    }

    let mut c : usize= 1;
    let mut f0 :usize= 0;
    let mut f1 :usize = 1;
    for i in 1..n+1 {
        //println!("i={}", i);
        let f : usize = f0 + f1;

        if let Some(count) = aset.remove(&i) {
            for _j in 0..count {
                c *= f;
                c %= MOD;
            }
        }

        if aset.len() == 0 {
            break;
        }

        f0 = f1;
        f1 = f % MOD;
    }
    
    return c;
}