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

def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result

result = 0

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

if M == 0:
    for i in range(math.floor((N-1)/2) + 1):
        result += cmb(N - List[M-1]-1-i,i) 
    result = result % 1000000007 
    print(result)

else:
    List = [int(input()) for i in range(M)]
    
    for i in range(math.floor((List[0]-1)/2) + 1):
        result += cmb(List[0]-1-i,i) 
            
    for i in range(M-1):
        if List[i+1] - List[i] == 1:
            result = 0
            break
        else:
            tmp = 0
            for j in range(math.floor((List[i+1]-List[i]-2)/2) + 1):
                tmp += cmb(List[i+1]-List[i]-2-j,j)
            result = result * tmp

    tmp = 0
    for i in range(math.floor((N - List[M-1]-1)/2) + 1):
        tmp += cmb(N - List[M-1]-1-i,i) 

    result = result * tmp
    result = result % 1000000007 
    print(result)