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: Accepted)

// 標準入力から一行を読み取り、指定の型に変換する
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()
}

// 標準入力から一行を読み取り、空白文字で分割し、各要素を指定の型に変換する関数
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

const MOD: u64 = 1_000_000_007;

fn main() {
    let nm: Vec<usize> = read_vec();
    let mut a: Vec<u64> = Vec::new();

    for i in 0..nm[1]
    {
        let ai: u64 = read();
        a.push(ai);
    }

    // 動的計画法
    let mut dp = vec![0_u64; nm[0] + 1];
    dp[0] = 1;

    // 崖崩れフラグ用変数
    let mut collapsed = 0_usize;

    for i in 1..dp.len() as usize
    {
        if collapsed < nm[1] && a[collapsed] == (i as u64)
        {
            // 崩壊している場合、この足場にたどり着くパターンは存在しない
            dp[i] = 0;
            collapsed += 1;
            continue;
        }

        if i == 1 { dp[1] = 1; continue; }

        dp[i] = (dp[i - 1] + dp[i - 2]) % MOD;
    }
    println!("{}", dp[nm[0]]);
}