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>
#include <string.h>
#include <stdbool.h>
#include <math.h>
long long mod=1000000007;

int MIN(int A,int B){
    return A<B?A:B;
}

int MAX(int A,int B){
    return A>B?A:B;
}

int main(void){
    long long n,m;
    scanf("%lld%lld",&n,&m);
    long long a[m+1];
    for (int i=0; i<m; i++){
        scanf("%lld",&a[i]);
    }
    a[m]=n+1;
    long long ans[n+1];
    for (int i=0; i<n; i++){
        ans[i]=0;
    }
    ans[0]=1;
    ans[1]=1;
    int count=0;
    if (a[0]==1){
        ans[1]=0;
        count++;
    }
    for (int i=2; i<=n; i++){
        if (i!=a[count]){
            ans[i]=(ans[i-2]+ans[i-1])%mod;
        } else {
            ans[i]=0;
            count++;
        }
    }
    printf("%lld\n",ans[n]%mod);
    return 0 ;
}