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::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: u64 = iterator.next().unwrap().parse().unwrap();
    let m: usize = iterator.next().unwrap().parse().unwrap();

    let mut prev: i64 = -1;
    let mut vec: Vec<i64> = Vec::with_capacity(m + 2);
    vec.push(-1);
    for _i in 0..m {
        let current = iterator.next().unwrap().parse().unwrap();
        if prev + 1 == current {
            // 連続したら到達不可能
            return String::from("0");
        }
        vec.push(current);
        prev = current;
    }
    vec.push((n + 1) as i64);

    let mut ans: u64 = 1;
    let mut memo: Vec<u64> = vec![0; 10_001];
    for i in 1..(m + 2) {
        ans *= fib((vec[i] - vec[i - 1] - 2) as usize, &mut memo) % MOD;
    }
    ans %= MOD;

    return ans.to_string();
}

const MOD: u64 = 1_000_000_007;

fn fib(n: usize, memo: &mut Vec<u64>) -> u64 {
    if memo[n] != 0 {
        return memo[n];
    }

    if n <= 1 {
        memo[n] = 1;
        return 1;
    }

    let result = (fib(n - 2, memo) + fib(n - 1, memo));
    memo[n] = result;
    result
}