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)

mod = 1000000007

def fib(n):
    a, b = 0, 1
    if n == 0:
        return a
    for _ in range(n - 1):
        a, b = b, a + b
    return b

# def feb(n):
#     if n == 0:
#         return 0
#     if n == 1:
#         return 1
#     k = (n + 1) / 2 if n % 2 else n / 2
#     fib_k = feb(k)
#     fib_k_1 = feb(k - 1)
#     return fib_k**2 + fib_k_1**2 if n % 2 else (2 * fib_k_1 + fib_k) * fib_k

    # if n==0:
    #     return 0
    # if n==1:
    #     return 1
    # else:
    #     return feb(n-1)+feb(n-2)
    # root = math.sqrt(5)
    # return int((1/root)*(((1+root)/2)**n - ((1-root)/2)**n))

def calculate(n, b):
    diff = [b[i+1] - b[i] - 1 for i in range(len(b)-1)]
    diff.insert(0, b[0])
    diff.append(n - b[-1])
    sum = 1
    for d in diff:
        if d == 0:
            return 0
        sum *= feb(d)%mod
        sum = sum%mod
    return sum


n, m = map(int, input().split())
b = []
for i in range(m):
    b.append(int(input()))

print(calculate(n, b))