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 <string.h>
#include <stdlib.h>
#include <math.h>
#define MAX(X, Y) ( ((X) > (Y))? (X) : (Y))
#define MIN(X, Y) (((X) < (Y))? (X) : (Y))
//　min
int main(void){
  int n, m;
  int a[100000];
  int MOD = 1000000007;
  int sum = 1;
  
  scanf("%d%d", &n, &m);

  for(int i = 1; i <= m; i++){
    scanf("%d", &a[i]);
    if(a[i] == a[i-1]){
      printf("0\n");
      return 0; 
    }
  }

  int cntm = 0;
  int mm = 0;
//  a[0] = 0;
//  a[1] = 1;
  for(int i = 2; i <= n; i++){
    if(i == 2 && a[mm] != i ){
      sum += 1;
    }else if(a[mm] == i){ 
   //   a[i] = a[i-1] +
      sum = sum + 1;
      mm++;
      cntm++;
      if(cntm == 2){
         printf("0\n");
        return 0;
      }
    }else{
      sum = sum + 2;
      cntm = 0;
    }    

    if(sum >= MOD){
      sum -= MOD;
     }
  }
  
  printf("%d\n", sum);

  return 0;
}