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)

use std::io;
use std::str;

pub struct Scanner<R> {
    reader: R,
    buffer: Vec<String>,
}

impl<R: io::BufRead> Scanner<R> {
    pub fn new(reader: R) -> Self {
        Scanner {
            reader: reader,
            buffer: Vec::new(),
        }
    }

    pub fn token<T: str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buffer.pop() {
                return token.parse().ok().expect("failed to parse token");
            }
            let mut input = String::new();
            self.reader.read_line(&mut input).expect("failed to read");
            self.buffer = input.split_whitespace().rev().map(String::from).collect();
        }
    }
}

static MODULO: usize = 1_000_000_007;

use io::Write;
fn main() {
    let (stdin, stdout) = (io::stdin(), io::stdout());
    let mut stdout = io::BufWriter::new(stdout);
    let mut scanner = Scanner::new(stdin.lock());

    let N: usize = scanner.token();
    let M: usize = scanner.token();

    //dp[i] := i段目への到達手段の全部の数
    //dp[0] = 1, dp[a_i] = 0;
    let mut dp: Vec<usize> = vec![0; N + 5];
    let mut notSafe: Vec<bool> = vec![false; N + 5];
    for _ in 1..M + 1 {
        notSafe[scanner.token::<usize>()] = true;
    }

    dp[0] = 1;
    if notSafe[1] == true {
        dp[1] = 0;
    } else {
        dp[1] = 1;
    }

    for i in 2..N + 2 {
        if notSafe[i] == true {
            continue;
        } else {
            dp[i] = (dp[i - 1] + dp[i - 2]) % MODULO;
        }
    }
    writeln!(&mut stdout, "{:?}", dp[N]);
}