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>

long fibo[100000];
long p;


int main(void) {
	int N, M;
	int i;

	scanf("%d%d", &N, &M);

	fibo[0] = 1;
	fibo[1] = 1;
	for (i = 2;i < N + 1;i++) {
		fibo[i] = fibo[i - 1] + fibo[i - 2];
	}

	for (i = 0;i < N + 1;i++) {
		fibo[i] %= 1000000007;
	}


	int a[M];

	for (i = 0;i < M;i++) {
		scanf("%d", &a[i]);
	}

	if (M == 0) {
		printf("%ld", fibo[N]);
		return 0;
	}

	int sa[M + 1];
	sa[0] = a[0];
	sa[M] = N - a[M - 1];

	if (M == 1) {}
	else {
		for (i = 0;i < M - 1;i++) {
			if (a[i + 1] == a[i] + 1) {

				printf("%d", 0);

				return 0;
			}
			else {
				sa[i + 1] = a[i + 1] - a[i] - 1;
			}
		}
	}
	p = 1;

	for (i = 0;i < M+1;i++) {
		
			p *= fibo[sa[i] - 1];
			p %= 1000000007;
		
	}

	printf("%ld", p % 1000000007);
	
	return 0;
	
}