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>

unsigned long ret[100002];

unsigned long pat(int sub) {
//  if      (sub==1) return 0;
//  else if (sub==2) return 1;
//  else             ret = pat(sub-1) + pat(sub-2);
//  if (ret>1000000007) return(ret-1000000007);
  int i;
  ret[1] = 0;
  ret[2] = 1;
  for (i=3;i<=sub;i++) {
    ret[i]=ret[i-1]+ret[i-2];
    if (ret[i]>1000000007) ret[i]-=1000000007;
  }
  return ret[sub];
}

int main() {
  int N, M, a[100002];
  int i;
  unsigned long tot;
  
  scanf ("%d %d", &N, &M);
  for (i=1;i<=M;i++) {
      scanf ("%d", &a[i]);
  }
  a[0] = -1;
  a[M+1] = N+1;
  
  tot = 1;
  
  for (i=1;i<=M+1;i++) {
    tot *= pat(a[i]-a[i-1]);
    if (tot>1000000007) tot-=1000000007;
  }
  printf ("%d", tot);
}