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: Time Limit Exceeded)

#include <stdio.h>
#include <stdint.h>
#define OK 0
#define NG 1
#define MOD 1000000007
  
int N;
int M;
static char A[100002];
static int64_t memo[100002];

int64_t search(int i) {
  if(memo[i] != 0) return memo[i];
  if(i >  N)     return 0;
  if(i == N)     return 1;
  if(A[i] == NG) return 0;

  int64_t ret0 = search(i+1);
  int64_t ret1 = search(i+2);
  int64_t ret = (ret0 + ret1);
  if(ret >= MOD) ret %= MOD;
  memo[i] = ret;
  return ret;
}

int main(void) {
  scanf("%d%d", &N, &M);
  for(int i = 0; i < M; i++) {
    int a;
    scanf("%d", &a);
    A[a] = NG;
  }
  int X = search(0);
  printf("%d\n", X);
  return 0;
}