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: Accepted)

#include <stdio.h>
#include <stdlib.h>

long fib(int n){
	if(n < 0)return 0;
	long a = 1, b = 1;
	long tmp;
	while(n){
		tmp = a;
		a += b;
		b = tmp;
		if(b > 1000000007)b -= 1000000007;
		if(a > 1000000007)a -= 1000000007;
		n--;
	}
	return b;
}

int main(void){
	//memo[0] = 1;
	int n, m;
	long ans = 1;
	int last = 0;
	int in;
	scanf("%d %d", &n, &m);
	for(int i = 0; i < m; i++){
		scanf("%d", &in);
		ans *= fib(in - last - 1);
		if(ans > 1000000007)ans %= 1000000007;
		last = in + 1;
	}
	ans *= fib(n - last);
	printf("%ld\n", ans % 1000000007);
	return 0;
}