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: Accepted)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

#define ll long long
#define rep(i, n) for (int i = 0; i < n; i++)

using namespace std;

int main()
{
	int n, m;
	cin >> n >> m;

	vector<int> dp(n + 1, 0);
	vector<bool> is_ok(n + 1, true);
	int res = 0;
	ll mod = 1e9 + 7;
	rep (i, m) {
		int tmp;
		cin >> tmp;
		is_ok[tmp] = false;
		if (tmp + 1 != n && is_ok[tmp + 1] == false) {
			cout << res << endl;
			return 0;
		}
	}

	dp[0] = 1;
	rep (i, n) {
		for (int j = 1; j <= 2; j++) {
			if (i + j < is_ok.size() && is_ok[i + j]) {
				dp[i + j] += dp[i];
				dp[i + j] %= mod;
			}
		}
	}

	cout << dp[n] << endl;

	return 0;
}