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: Wrong Answer)

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()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn fib(x: u64) -> u64 {
    let mut a = 1;
    let mut b = 1;

    for _ in 1..x {
        b = a + b;
        a = b - a;
    }
    a
}

#[test]
fn test_fib() {
    assert_eq!(fib(1), 1);
    assert_eq!(fib(2), 1);
    assert_eq!(fib(3), 2);
    assert_eq!(fib(4), 3);
    assert_eq!(fib(5), 5);
    assert_eq!(fib(6), 8);
    assert_eq!(fib(7), 13);
}

fn run(n: u64, m: u64, a: &mut Vec<u64>) {
    let mut b = Vec::new();

    // check
    for i in 0..m {
        let j = i as usize;

        if j == 0 {
            if a[j] == 1 {
                continue;
            } else {
                b.push(a[0])
            }
        }

        if j < (m - 1) as usize {
            let sub = a[j + 1] - a[j];
            if sub == 1 {
                println!("0");
                return;
            } else {
                b.push(sub);
            }
        } else {
            let sub = n - a[j];
            b.push(sub);
        }
    }

    let ans = b.iter().map(|&x| fib(x)).fold(1, |acc, y| acc * y);
    println!("{}", ans % 1000000007);
}

fn main() {
    let v = read_vec::<u64>();
    let n = v[0];
    let m = v[1];
    let mut a = Vec::new();
    for i in 0..m {
        let ai = read::<u64>();
        a.push(ai);
    }

    run(n, m, &mut a);
}