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)

n,m=map(int,input().split())
l=[]
def nibutan(x,l):
    low=0
    high=len(l)-1
    while low<=high:
      mid=(low+high)//2
      guess=l[mid]
      if guess==x:
         return True
      elif guess>x:
          high=mid-1
      elif guess<x:
          low=mid+1
    return False
for i in range(m):
  l.append(int(input()))
l1=[0 for i in range(n)]
if 1 in l:
  l1[0]=0
else:
  l1[0]=1
if 2 in l:
  l1[1]=0
elif 1 in l:
  l1[1]=1
else:
  l1[1]=2

if n>=3:
  for i in range(3,n+1): 
    if nibutan(i,l):
      pass
    else:
      l1[i-1]=(l1[i-2]+l1[i-3])%(((10**9)+7))
print(l1[n-1])