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: Runtime Error)

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        a: [u128; m]
    };
    let a: Vec<u128> = a;

    let base = (10i32.pow(9) + 7) as u128;
    let mut result = 1;

    let f = |x: u128| -> u128 {
        if x <= 2 {
            return 1;
        } else {
            let n = x - 2;
            let i = 2;
            let tmp = (n * (n - 1)) / 2;

            return i + tmp;
        }
    };

    let mut prev = n as u128;

    for i in 0..=m {
        if i < m {
            if prev + 1 == a[i] {
                result = 0;
                break;
            }
        }

        if i == 0 {
            let x = a[i];
            let r = f(x);
            result *= r;
            result %= base;
            prev = a[i];
        } else if i == m {
            let x = n as u128 - a[m as usize - 1];
            let r = f(x);
            result *= r;
            result %= base;
        } else {
            let x = a[i] - a[i - 1] - 1;
            let r = f(x);
            result *= r;
            result %= base;
            prev = a[i];
        }
    }

    println!("{}", result % base);
}