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 comb(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)]
check = a[:]

a.insert(0,0)
a.append(n)

c = 0
d = [0]*(m+1)
for j in range(m+1):
    c = a[j+1] - a[j] -1
    
    e, f = 0,0
    while c - e*2 >= 0:
        f += comb(c-e,c-2*e)
        e +=1
    d[j] = f
    
    


    
answer = 1
for number in range(m+1):
    answer *= d[number]

ch = 1
for k in range(m-1):
    if check[k] == check[k+1] - 1:
        ch =0


if ch == 0:
    print(0)
else:
    print(answer % (10**9+7))