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)

def fib_memo(n):
    memo=["EMPTY"]*(n+1)
    def _fib(n):
        if n == 1:
            return 0
        elif n == 2:
            return 1
        elif memo[n] != "EMPTY":
            return memo[n]
        else:
            memo[n] = _fib(n-1)+_fib(n-2)
            return memo[n]
    return _fib(n)
def fib(n):
    f = ((1 + 5**0.5) / 2)**n / 5**0.5 + 0.5
    return int(f)
  
n,m=map(int,input().split())
a=[int(input()) for i in range(m)]
if a:
  cnt=fib(a[0]+1)*fib(n-a[m-1]+1)
  for i in range(1,m):
    cnt*=fib(a[i]-a[i-1])
  print(cnt%(10**9+7))
else:
  print(fib_memo(n+2)%(10**9+7))