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 Python (3.8.2) (judge verdict: Runtime Error)

def resolve():
    '''
    code here
    '''
    from functools import lru_cache

    N, M = [int(item) for item in input().split()]
    As = [int(input()) for _ in range(M)]
    memo = [1 for _ in range(N+1)]

    for item in As:
        memo[item] = 0

    res_list = []
    for i in range(1,N+1):
        if i == 1 and memo[i] == 0:
            memo[i] = 0
            res_list.append(2)
        elif memo[i] == 0:
            memo[i] = 0
            res_list.append(memo[i-1])
        else:
            memo[i] += memo[i-1]
    else:
        res_list.append(memo[N])

    
    @lru_cache
    def cal(num):
        if num <= 1:
            return 0
        elif num == 2:
            return 1
        elif num == 3:
            return 2
        else:
            return cal(num-1) + cal(num-2)
    
    res = 1
    for item in res_list:
        res *= cal(item)
    print(res % (10**9 + 7))



if __name__ == "__main__":
    resolve()