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 = map(int, input().split())
A = [int(input()) for i in range(m)]
if m == 0:
  Fib = [1,2]
  for i in range(2,n):
    Fib.append(Fib[i-2]+Fib[i-1])
  print(Fib)
  print(Fib[n-1])
  exit()

B = [A[i+1]- A[i] for i in range(m-1)]
B.insert(0,A[0]+1)
B.append(n+1-A[m-1])

M = max(A)

Fib = [0,1]
for i in range(2,M+10):
  Fib.append(Fib[i-2]+Fib[i-1])

ans = 1
for i in range(len(B)):
  ans = (ans * Fib[B[i]-1])%1000000007
  
print(ans)