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)

from collections import deque

def num_way(stair):
  memo = ["EMPTY"]*(stair+1)
  def _fib(stair):
    if stair == 1 or stair == 0:
      return 1
    elif stair == 2:
      return 2
    elif memo[stair] != "EMPTY":
      return memo[stair]
    else:
      memo[stair] = _fib(stair-1)+_fib(stair-2)
      return memo[stair]
  return _fib(stair)

N, M = map(int,input().split())
a = deque([0])
path_poss = 1
ans = 1
for m in range(M):
  start = a.popleft()
  buff = int(input())
  end = buff-1
  if (end-start) <= -1:
    path_poss = 0
    break
  a.append(buff+1)
  ans *= num_way(end-start)
  ans %= 1000000007

if path_poss == 0:
  print(0)
else:
  start = a.popleft()
  end = N
  if (end-start) <= -1:
    path_poss = 0
  if path_poss == 0:
    print(0)
  else:
  	print(ans%1000000007)