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)

const TOP: u64 = 1_000_000_007;

pub struct Poper<'a> {
	iter: std::str::SplitWhitespace<'a>,
}

impl<'a> Poper<'a> {
	pub fn new(iter: std::str::SplitWhitespace) -> Poper {
		Poper { iter: iter }
	}
	pub fn read<T: std::str::FromStr>(&mut self) -> T
	where
		<T as std::str::FromStr>::Err: std::fmt::Debug,
	{
		self.iter.next().unwrap().parse().unwrap()
	}
}

// use std::collections::BTreeMap;

fn main() {
	let input = {
		use std::io::Read;
		let mut s = String::new();
		std::io::stdin().read_to_string(&mut s).unwrap();
		s
	};
	let mut iter = Poper::new(input.split_whitespace());

	let n: usize = iter.read();
	let m: usize = iter.read();

	let mut map: Vec<bool> = vec![true; n + 1];

	for _ in 0..m {
		let c: usize = iter.read();
		map[c] = false;
	}

	let mut count: Vec<u64> = vec![0; n + 1];

	count[0] = 1;
	if map[1] {
		count[1] = 1;
	}

	if 1 < n {
		for c in 2..n + 1 {
			if map[c] {
				count[c] = (count[c - 2] + count[c - 1]) % TOP;
			}
		}
	}

	println!("{}", count[n]);
}