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)

n, m=map(int, input().split())
a=[0]*m
for i in range(m):
    a[i] = int(input())
ans = [0]*(n+1)
idx=0
if a[0]==1:
    idx+=1
    ans[1] = 0
    if n==1:
        pass
    elif m>=2 and a[1]==2:
        idx+=1
        ans[2]=0
    else:
        ans[2]=1
else:
    ans[1] = 1
    if n==1:
        pass
    elif a[0]==2:
        idx+=1
        ans[2]=0
    else:
        ans[2]=2

for k in range(3,n+1):
    if idx>=m or a[idx]!=k:
        ans[k]=ans[k-1]+ans[k-2]
        if ans[k]>=10**9+7:
            ans[k] %= 10**9+7
    else:
        ans[k]=0
        idx+=1

print(ans[n])