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)

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let m: usize = iter.next().unwrap().parse().unwrap();

    let mut a_s = Vec::with_capacity(n);

    let mut a: usize = 200000;
    if m != 0 {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        a = buf.trim().parse().unwrap();
    }
    else {
    }
    let mut cur_m = 1;

    for i in 0..n {
        // println!("{} {}", i, a);
        if i == a {
            a_s.push(false);

            if cur_m < m {
                let mut buf = String::new();
                std::io::stdin().read_line(&mut buf).unwrap();
                a = buf.trim().parse().unwrap();
                cur_m += 1;
            }
        }
        else {
            a_s.push(true);
        }
    }

    let mod_n = 1000000007usize;

    let mut dp = vec![0; n];

    for i in (0..n).rev() {
        // println!("{} {}", i, a_s[i]);

        if a_s[i] == false {
            continue;
        }

        if i == n-1 {
            dp[i] = 1;
        }
        else if i == n-2 {
            dp[i] = dp[i+1] + 1;
        }
        else {
            dp[i] = (dp[i+1] + dp[i+2]) % mod_n;
        }

        // println!("  {} {}", sum, sum_local);
    }

    println!("{}", dp[0]);
}