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: Wrong Answer)

import math


def combi(a, b):
    ans = math.factorial(a) / (math.factorial(a - b) * math.factorial(b))
    ans=int(ans)
    return ans

N,M=map(int,input().split())

mod=10**9+7

if N==1:
    print(1)
    exit()

if M==0:
    a=N-1

a0=-1
cnt=[]
for i in range(M):
    a=int(input())
    n=(a-1)-(a0+1)
    if a-a0==1:
        print(0)
        exit()
    c=0
    for k in range(n // 2 + 1):
        c += combi(n - k, k) % mod
    cnt.append(c)
    a0=a

if not a==N-1:
    a=N-1
    n = a - a0
    c = 0
    for k in range(n // 2 + 1):
        c += combi(n - k, k) % mod
    cnt.append(c)

ans=1
for i in range(len(cnt)):
    ans*=cnt[i]
    ans=ans%mod

print(ans)