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
import numpy as np

def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

N, M = map(int, input().split())
A = [int(input()) for i in range(M)]

diff = np.array(A)[1:] - np.array(A)[:-1]
if any(diff == 1) :
    print(0)
else :
    S = []
    A.insert(0, 0)
    A.insert(N-1, N)
    #print(A)
    D = list(np.array(A)[1:] - np.array(A)[:-1])
    for d in range(1, len(D) - 1) :
        D[d] -= 1
    R = []
    #print(D)
    for d in D :
        P = d - 1
        K = int(P / 2)
        T = 1
        for k in range(1, K+1) :
            T += combinations_count(P - k, k)
        R.append(T)
    ans = R[0]
    #print(R)
    for r in R[1:] :
        #print(ans)
        ans = ans * r % (10 ** 9 + 7)
    print(ans)