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 (7.3.0) (judge verdict: Time Limit Exceeded)

#create date: 2020-07-25 09:13

import sys
stdin = sys.stdin
mod = 10**9+7

def ns(): return stdin.readline().rstrip()
def ni(): return int(ns())
def na(): return list(map(int, stdin.readline().split()))

def main():
    n, m = na()
    a = list()
    for i in range(m):
        a.append(ni())

    dp = [0] * (10**5+1)
    dp[0] = 1
    if not 1 in a: dp[1] = 1
    for i in range(2, n+1):
        if i in a:
            dp[i] = 0
        else:
            dp[i] = (dp[i-2] + dp[i-1]) % mod
    print(dp[n])

if __name__ == "__main__":
    main()