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 <iostream>
#include <math.h>

using namespace std;

int search(int x) {
	if (x <= 2)
		return 1;
	return search(x-2)+search(x-1);
}

int main() {
	long long n = 0, m = 0, ans = 1;
	cin >> n >> m;
	bool* a = new bool[n+2];
	for (int i = 0; i <= n; ++i) {
		a[i] = true;
	}
	a[n + 1] = false;
	int tmp;
	for (int i = 0; i < m; ++i) {
		cin >> tmp;
		a[tmp] = false;
	}
	tmp = 0;
	for (int i = 0; i <= n+1; ++i) {
		if (a[i]) {
			++tmp;
		}
		else {
			if (tmp==0) {
				ans = 0;
				break;
			}
			ans *= search(tmp);
			tmp = 0;
		}
	}
	cout <<ans%1000000007;
	return 0;
}