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 (3.4.3) (judge verdict: Runtime Error)

import fractions

N, M = map(int,input().split())
a=[-1]
for i in range(M):
    a.append(int(input()))
a.append(N+1)
#print(a)
D=[]
for i in range(M+1):
    D.append((a[i+1]-1)-(a[i]+1))
#print(D)
def nCk(n, k):
    return fractions.factorial(n)/(fractions.factorial(k)*fractions.factorial(n-k))
ans=1
for i in range(len(D)):
    if i !=len(D) and i!=0 and D[i]==0:
        temp = 0
    else:
        temp = 0
        for j in range(D[i]//2+1):
            temp += nCk(D[i]-j,j)
#    print(temp)
    ans=(ans*temp)%1000000007
print(int(ans%1000000007))