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: Runtime Error)

use std::io::stdin;

fn abs(a: isize) -> isize {
    if a < 0 { -a } else { a }
}

fn main() {
    let mut n = String::new();
    stdin().read_line(&mut n).unwrap();
    let n: usize = n.trim().parse().unwrap();

    let mut ws = String::new();
    stdin().read_line(&mut ws).unwrap();
    let ws: Vec<isize> = ws.trim().split_whitespace().flat_map(str::parse).collect();

    let mut l = 0;
    let mut r: isize = ws.clone().into_iter().sum();
    let mut best = r;
    for w in ws.into_iter() {
        l += w;
        r -= w;
        let a = abs(l - r);
        if a < best {
            best = a;
        }
    }
    println!("{}", best);
}