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)

N,M = list(map(int,input().split()))
lst = []
for i in range(M):
  a = int(input())
  lst.append(a)
#print(lst)

for i in range(M-1):
  if lst[i] == lst[i+1]:
    print("0")
    exit()

if 1 in lst and not 3 in lst:
  lst2 = [0,1,1]
  for j in range(4,N+1):
    #print(j)
    if j in lst:
      lst2.append(0)
    else:
      #print(lst2,lst2[-1],lst2[-2])
      lst2.append(lst2[-1]+lst2[-2])
elif 2 in lst:
  lst2 = [1,0,1]
  for j in range(4,N+1):
    #print(j)
    if j in lst:
      lst2.append(0)
    else:
      #print(lst2,lst2[-1],lst2[-2])
      lst2.append(lst2[-1]+lst2[-2])
elif 3 in lst and not 1 in lst:
  lst2 = [1,2,0]
  for j in range(4,N+1):
    #print(j)
    if j in lst:
      lst2.append(0)
    else:
      #print(lst2,lst2[-1],lst2[-2])
      lst2.append(lst2[-1]+lst2[-2])
elif 1 in lst and 3 in lst:
  lst2 = [0,1,0]
  for j in range(4,N+1):
    #print(j)
    if j in lst:
      lst2.append(0)
    else:
      #print(lst2,lst2[-1],lst2[-2])
      lst2.append(lst2[-1]+lst2[-2])
else:
  lst2 = [1,2,3]
  for j in range(4,N+1):
    #print(j)
    if j in lst:
      lst2.append(0)
    else:
      #print(lst2,lst2[-1],lst2[-2])
      lst2.append(lst2[-1]+lst2[-2])
#print(lst2)
#print(lst[-1])
#print(lst2[-1])
print(lst2[-1]%1000000007)