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)

def fib(n):
    a1 = 2
    a2 = 1 
    if n==2:
        return 2
    elif n==1:
        return 1
    else:
        count = 1
        for i in range(n-2):
            count = a1 + a2
            a2 = a1
            a1 = count
        return count
        
N,M = list(map(int,input().split()))
ans = 1
z = False

if M == 0:
    ans *= fib(N)
    print(ans) 
else:
    a = [int(input()) for _ in range(M)]

    for i in range(M):
        if i != 0:
            if a[i]-a[i-1] != 1:
                ans *= fib(a[i]-a[i-1]-2)
            else:
                z = True
                break
        else:
            ans *= fib(a[i]-1)

    ans *= fib(N-a[-1]-1)

    if z:
        print(0)
    else:
        print(str(ans%1000000007))