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: Accepted)

import math
 
n,m = list(map(int, input().split()))

dan=[]

for i in range(m):
    b=list(map(int, input().split()))
    dan.append(b[0])

fib=[0 for i in range(n+2)]
fib[1]=1
fib[2]=2

for ii in range(n-1):
    i=ii+3
    fib[i]=(fib[i-1]+fib[i-2])%1000000007
    
#print(fib,dan)

eachans=[]

if(m==0):
    print(fib[n])

if(m>=1):
    if(dan[0]!=1):
        eachans.append(fib[dan[0]-1])

    for i in range(m-1):
        if(dan[i+1]-dan[i]-2 == 0):
            eachans.append(1)
        elif(dan[i+1]-dan[i]-2 == -1):
            eachans.append(0)
        else:
            eachans.append(fib[dan[i+1]-dan[i]-2])
        #print(dan[i+1]-dan[i]-1)

if(m>=1):
    if(dan[-1]!=n-1):
        eachans.append(fib[n-dan[-1]-1])
    
if(m>=1):
    #print(eachans)
    ans=1
    for i in range(len(eachans)):
        ans = ans*eachans[i]%1000000007

    print(ans)