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>

#define INF 0x7f
#define MOD 1000000007

int max(int a,int b)
{
    if(a >= b)
    {
        return a;
    }
    else
    {
        return b;
    }
}

int main()
{
    int n,m,a[100000],mcount = 0;
    scanf("%d %d",&n,&m);
    for (int i = 0; i < m; i++)
    {
        scanf("%d",&a[i]);
    }
    
    int dp[100010];
    memset(dp,0,sizeof(dp));

    dp[0] = 1;

    for (int i = 1; i <= n ; i++)
    {
        if(i == a[mcount]){
            mcount++;
            dp[i] = 0;
        }
        else
        {
            if(i >= 2)dp[i] = dp[i - 2];
            dp[i] += dp[i - 1];
            dp[i] = dp[i] % MOD;
        }
        for (int j = 0; j <= n; j++)
        {
            printf("%d ",dp[j]);
        }
        printf("\n");
        
    }
    printf("%d",dp[n]);
}