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)

use std::io;
use std::str::FromStr;
use std::collections::HashMap;

fn input_int_tuple() -> (u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1])
}

fn input<T:FromStr>() -> T {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.trim().parse().ok().unwrap()
}

fn main() {
    let (n, m) = input_int_tuple();
    let mut a_vec: Vec<u64> = Vec::new();

    for i in 0..m {
        let a: u64 = input();
        a_vec.push(a);
    }

    if m == 0 {
        let fibonacci_vec = fibonacci(n);        
        println!("{}", fibonacci_vec[n as usize - 1]);
        return;
    }

    let mut max_dist = a_vec[0];
    for i in 1..a_vec.len() {
        if a_vec[i as usize] - a_vec[i as usize - 1] > max_dist {
            max_dist = a_vec[i as usize] - a_vec[i as usize - 1];
        }
    }
    let fibonacci_vec = fibonacci(max_dist);

    let mut now = 0;
    let mut sum = 1;
    for a in &a_vec {
        let distance = *a - now;
        if distance == 0 {
            println!("0");
            return;
        }
        sum *= fibonacci_vec[(distance - 1) as usize];
        if sum > 1000000007 {
            sum %= 1000000007;
        }
        // println!("sum = {}", sum);
        now = *a + 1;
    }
    sum *= fibonacci_vec[(n - now) as usize];
    // println!("{:?}", a_vec);
    if sum > 1000000007 {
        sum %= 1000000007;
    }
    println!("{}", sum);
}

fn fibonacci(max: u64) -> Vec<u64> {
    let mut fibonacci_vec: Vec<u64> = Vec::new();
    for i in 0..max + 1 {
        if i == 0 || i == 1 {
            fibonacci_vec.push(1);
            continue;
        }        
        let n = fibonacci_vec[i as usize -1] + fibonacci_vec[i as usize -2];
        fibonacci_vec.push(n);
    }
    fibonacci_vec
}