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)

use std::io::*;
use std::str::FromStr;

const MOD: usize = 1_000_000_007;

fn main() {
    let n: usize = read();
    let m: usize = read();
    let a: Vec<usize> = (0..m).map(|_| read()).collect();

    let mut dp: Vec<usize> = vec![0; n+1];
    dp[0] = 1;
    dp[1] = 1;
    if n > 1 {
        dp[2] = 2;
    }
    for i in 3..n+1 {
        dp[i] = dp[i-1] + dp[i-2];
        dp[i] %= MOD;
        //println!("{}", dp[i]);
    }

    if m == 0 {
        println!("{}", dp[n]);
        return;
    }

    let mut ok = true;
    for i in 0..m-1 {
        if a[i+1] - a[i] == 1 {
            ok = false;
        }
    }
    if !ok {
        println!("0");
        return;
    }

    let mut ans: usize = 1;
    if a[0] > 1 {
        ans = dp[a[0]-1];
    }
    for i in 1..m {
        if a[i] > a[i-1] + 1 {
            ans *= dp[a[i] - a[i-1]-2];
            ans %= MOD;
        }
    }
    ans *= dp[n-1 - a[m-1]];
    ans %= MOD;
    println!("{}", ans);
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}