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::*;

const SP: u8 = b' ';
const LF: u8 = b'\n';

struct CharacterInput<'a> {
    locked_stdin: StdinLock<'a>,
    bytes_buffer: Vec<u8>,
}

impl<'a> CharacterInput<'a> {
    fn read(&mut self, delimiter: u8) -> &[u8] {
        self.bytes_buffer.clear();

        let mut len = self
            .locked_stdin
            .read_until(delimiter, &mut self.bytes_buffer)
            .unwrap();

        if len > 0 {
            len -= 1;
        }

        &self.bytes_buffer[0..len]
    }

    fn scan_u(&mut self, delimiter: u8) -> u32 {
        self.read(delimiter)
            .into_iter()
            .fold(0, |accumulator, byte| {
                (byte - b'0') as u32 + accumulator * 10
            })
    }
}

fn create_cin<'a>(input: StdinLock<'a>, buffer_capacity: usize) -> CharacterInput {
    CharacterInput {
        locked_stdin: input,
        bytes_buffer: Vec::with_capacity(buffer_capacity),
    }
}

fn println<T: std::string::ToString>(s: T) {
    println!("{}", s.to_string());
}

// ------------------------------------------------------------------------

fn get_pattern_count(stair_no: usize, table: &mut Vec<Option<u32>>) -> u32 {
    table[stair_no].unwrap_or_else(|| match stair_no {
        0 => 1,
        1 => {
            table[1] = Some(1);
            1
        }
        _ => {
            let pattern_count =
                (get_pattern_count(stair_no - 2, table) + get_pattern_count(stair_no - 1, table)) % 1000000007;
            table[stair_no] = Some(pattern_count);
            pattern_count
        }
    })
}

fn main() {
    let cin = stdin();
    let cin = &mut create_cin(cin.lock(), 32);

    let n = cin.scan_u(SP) as usize;
    let m = cin.scan_u(LF) as usize;

    let mut table = vec![None as Option<u32>; n + 1];
    table[0] = Some(1);

    for _ in 0..m {
        table[cin.scan_u(LF) as usize] = Some(0);
    }

    println(get_pattern_count(n, &mut table));
}