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: Runtime Error)

N,M=map(int,input().split())
a=list(int(input()) for _ in range(M) )
ans=0
ansn1=0
ansn2=0
mod=1000000007
A=a[0]
for i in range(N):

    if i>=2 and  i+1 < A:
        ans=(ansn1+ansn2)%mod
        ansn2 = ansn1
        ansn1=ans
        continue

    elif i>=2 and  i+1 > A:
        ans=(ansn1+ansn2)%mod
        ansn2 = ansn1
        ansn1=ans
        if a.index(A)+1<=M-1:
            A=a[a.index(A)+1]
        else:
            A=mod
        continue

    elif i+1 == A:
        ans = 0
        ansn2 = ansn1
        ansn1 = ans
        if a.index(A) + 1 <= M - 1:
            A = a[a.index(A) + 1]
        else:
            A=mod
        continue


    if i==0:
        if i+1 not in a:
            ans=1
            ansn2 = 0
            ansn1=ans


    elif i==1:
        if i+1 not in a:
            ans=1+ansn1
            ansn2 = ansn1
            ansn1=ans
        else:
            ans=0
            ansn2=ansn1
            ansn1=ans


print(ans)