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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include "bits/stdc++.h"
#define rep(i,N) for (int (i) = 0; (i) < (N); (i)++)
#define debug(var) std::cout << #var << " : " << var << std::endl;

int main() {

	std::cin.tie(nullptr); std::ios::sync_with_stdio(false);

	unsigned long long ans = 0;
	int N, M; std::cin >> N >> M;
	std::vector<int> a; rep(i, M) {
		int tmp; std::cin >> tmp;
		a.push_back(tmp);
	}
	
	int current = 0;
	bool flag = false;

	while (current <= N) {
		auto plus1 = std::find(a.begin(), a.end(), current + 1);
		auto plus2 = std::find(a.begin(), a.end(), current + 2);
		if (plus1 == a.end() && plus2 == a.end()) {
			if (ans == 0)ans = 2;
			else ans *= 2;
			current += 2;
		}
		else if (plus1 == a.end()) {
			current++;
		}
		else if (plus2 == a.end()) {
			current += 2;
		}
		else {
			flag = true;
			std::cout << 0;
			break;
		}
		ans %= 1000000007;
	}

	if (!flag)std::cout << ans;

	return 0;
}