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 <math.h>
#include <limits.h>
#include <string.h>
#define ll long long int




int main()
{

    ll N, M ;
    scanf("%lld %lld",&N,&M);
    ll d = N+1;
    ll array[d];
    memset(array,0,sizeof(array[0])*d);
    array[0]=1;
    array[1]=1;
    ll idx=0;
    ll a[M];
    for (ll i = 0; i<M; i++)
    {
        scanf("%lld",&a[i]);
        if (a[i]==1)
        {
            array[1]=0;
            idx++;
        }
    }


    for (ll i = 2; i<=N; i++)
    {
        if (i==a[idx] && idx<M)
        {
            idx++;
            continue;

        }
        array[i]=array[i-1]+array[i-2];
        array[i]=array[i]%1000000007;
    }


    printf("%lld",array[N]% 1000000007);



    return 0;
}