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)

z = input().split()
z = [ int(x) for x in z]
broken = []
for i in range(z[1]):
    broken.append(input())
#print(broken)

max_step = z[0] 
import numpy as np

all_possible = []

def steps(cand):
  tmp = np.zeros_like(cand)
  for j in range(len(cand)):
    tmp[j] = sum(cand[:j+1])
  return tmp


count = 0
all_count = 0

for i in range(int(max_step/2), max_step+1):
    #iは段の数
        
    import itertools
    A = [1 , 2 ]
    for v in itertools.product(A, repeat = i):
      if sum(v) == max_step:
        all_count += 1
        for b in broken:
          if list(v).count(int(b)) > 0:
            count += 1
        
#         all_possible.append(steps(v))
          
 

#for i in range(len(all_possible)):
  #all_possible[i] = steps(all_possible[i])
#  all_count += 1
 # for b in broken:
    #print( list(all_possible[i]).count(int(b)))
  #  if  list(all_possible[i]).count(int(b)) > 0:
    #    all_possible[i]= [0,0]
       # count += 1
        
print((all_count - count)%1000000007)