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())

MOD = 10 ** 9 + 7
a = []
flag = True
for i in range(M):
  tmp = int(input())
  if i != 0 and tmp == a[-1] + 1:
    print(0)
    flag = False
    break
  a.append(tmp)

if flag:
  max_dis = 0
  dis = []
  for i in range(len(a)):
    if i == 0:
      dis.append(a[i])
    else:
      dis.append(a[i] - a[i - 1] - 1)
    max_dis = max(max_dis, dis[-1])
  max_dis = max(max_dis, N - a[-1])
  
  fib = [1, 1]
  for _ in range(max_dis):
    fib.append(fib[-1] + fib[-2])
  ans = 1
  for d in dis:
    ans = (ans * fib[d - 1])
  ans *= fib[N - a[-1] - 1]
  
  print(ans % MOD)