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: Time Limit Exceeded)

import sys
#from scipy.special import comb
from scipy.misc import comb

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

A = [0]*M

for i in range(M):
    A[i] = int(input())

A.append(N+1)

def step_comb(L):
    c = 0
    if L==1 or L == 0:
        c = 1
    else:
        for i in range(L//2 +1):
            j = L - 2*i
            c += comb(j+i, i, exact=True)
    return c

total_comb = 1
NOW = 0
for a in A:
    if NOW == a:
        print(0)
        sys.exit()
    L = a-1-NOW
    total_comb *= step_comb(L)
    NOW = a + 1
    
print(total_comb % 1000000007 )