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)

n,m = map(int,input().split())
li = [int(input()) for i in range(m)]
p = 1000000007
ans = 0

steps = [0]*(max(10,n+1))
steps[1] = 1
steps[2] = 2
for i in range(3,n+1):
  steps[i] = (steps[i-1] + steps[i-2])%p
if m == 0:
  print(steps[n])
else:
  if li[0] == 1:
    ans += 1
  else:
    ans += steps[li[0]-1]%p

  for i in range(m-1):
    if li[i+1] == li[i]:
      continue
    elif li[i+1] - li[i] == 1:
      ans = 0
    elif li[i+1] - li[i] == 2:
      continue
    else:
      ans *= steps[li[i+1]-li[i]-2]
      ans %= p

  if li[m-1] == n-1: 
    print(ans)
  else:
    print((ans*steps[n-li[m-1]-1])%p)