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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10**6)
large_p = 10**9 + 7
a = []
kazu_memo = {}
def f(target_step):
    global kazu_memo
    #print(target_step)
    if target_step in a:
        return 0
    elif target_step < 0:
        return 0
    elif target_step == 0:
        return 1
    else:
        if kazu_memo[target_step] > 0:
            return kazu_memo[target_step]
        else:
            kazu_tmp = 0
            kazu_tmp += f(target_step - 1)
            kazu_tmp += f(target_step - 2)
            kazu_memo[target_step] = kazu_tmp % large_p
            return kazu_tmp % large_p

def main():
    global a, kazu_memo
    n, m = map(int, input().split())
    a = [int(input()) for _ in range(m)]

    kazu_memo = {e: -1 for e in range(1, n + 1)}
    r = f(n)
    print(r % large_p)


if __name__ == '__main__':
    main()