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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdbool.h>

int main() {
	long long int i, j = 1, n, m, fibo = 1, fi = 1, f = 0, a[100000], sum = 1;
	bool flag = true;

	// 壊れている床の数
	scanf("%lld %lld", &n, &m);

	// 壊れている床の段
	a[0] = -1;
	for (i = 1; i <= m; i++) {
		scanf("%lld", &a[i]);
	}

	// 登れるかチェック
	for (i = 1; i <= m; i++) {
		if (a[i] - a[i - 1] == 1) {
			printf("%d\n",0);
			return 0;
		}
	}

	for (i = 1; i <= n; i++) {
		flag = true;
		for (j = 1; j <= m; j++) {
			if (a[j] == i) {
				a[j] = 0;
				flag = false;
				sum = (sum * fibo) % 1000000007;
				fibo = 1;
				fi = 1;
				f = 0;
				i++;
				break;
			}
		}
		if (flag == true) {
			fibo = fi + f;
			f = fi;
			fi = fibo;
		}
	}
	sum = (sum * fibo) % 1000000007;

	printf("%lld\n", sum % 1000000007);

	return 0;
}