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<stdlib.h>
#include<string.h>

int main()
{
	long long waru = 1000000007;
	long long N, M;
	long long i;
	long long ans = 1;
	long long(*a) = (long long(*))malloc(100010 * sizeof(long long));
	long long(*s) = (long long(*))malloc(100010 * sizeof(long long));
	long long(*fib)= (long long(*))malloc(100010 * sizeof(long long));
	scanf("%lld%lld", &N, &M);
	for (i = 0;i < M;i++)scanf("%lld", &a[i]);
	a[M] = N+1;
	s[0] = a[0] - 1;
	fib[0] = 1;
	fib[1] = 1;
	
	for (i = 1;i <= M;i++)
	{
		s[i] = a[i] - a[i-1]-1;
	
		
		if (s[i] <= 0)/*移動不可能*/
		{
			printf("0\n");
			return 0;
		}
	}
	for (i = 2;i < N;i++)
	{
		fib[i] = fib[i - 1] + fib[i - 2];
	
	}
	ans *= fib[s[0]];
	for (i = 1;i <= M;i++)
	{
		
		ans *= fib[s[i]-1];
		
	}
	printf("%lld\n", ans%waru);
	return 0;
}