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 math
N, M = map(int,input().split())
a = [int(input()) for i in range(M)]
b = [-1]+ a+ [N+1]
def combination(n, k):
    result = 1
    for i in range(n - k + 1, n + 1):
        result *= i
    for i in range(1, k + 1):
        result /= i
    return result

def fibonacci(k):
    k = k + 1
    result = 0
    for i in range(1, int(math.ceil(k / 2.0) + 1)):
        result += combination(k, 2 * i - 1) * pow(5, i - 1)
    return int(result / pow(2, k - 1))

def combi(d):
    if d < 0:
        return 0
    elif 0 <= d <= 1:
        return 1
    else:
        return fibonacci(d)
ans = 1
for i in range(len(b)-1):
    ans= (ans*combi(b[i+1]-b[i]-2))%1000000007
print(ans)