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: Time Limit Exceeded)

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

long long int func(int d);

int main(){
	
	int i, j, n, m, d;
	long long int ans = 1, mod = 1000000007;
	
	scanf("%d %d", &n, &m);
	
	int a[m + 2];
	
	a[0] = -1;
	a[m + 1] = n + 1;
	
	for(i = 1; i <= m; i++)
		scanf("%d", &a[i]);
	
	for(i = 0; i <= m; i++){
		// 前の穴の次のマスから、次の穴の前のマスまでの距離をdとする
		d = a[i + 1] - a[i] - 2;
		// dだけ移動する方法の総数を求める (d == 0のときは1マスしかないので1通りしかない)
		if(d > 0){
			ans *= func(d);
			ans %= mod;
		}else if(d < 0){
			ans = 0;
			break;
		}
	}
	
	
	printf("%lld", ans);
	
	return 0;
}

long long int func(int d){
	
	if (d <= 0)
		return 0;
	
	else if(d < 2)
		return 1;
	
	else if(d < 4)
		return d;
	
	else
		return (func(d - 2) * 2 + func(d - 3));
}