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)

d = {}


def calc_step_combination(num):
    if num <= 0:
        return 0
    if num == 1 or num == 2:
        return 1
    if num in d:
        return d[num]
    res = calc_step_combination(num - 1) + calc_step_combination(num - 2)
    d[num] = res
    return res


def sol(n, a_list):
    if len(a_list) == 0:
        print(0)
        return
    step_batch = []
    batch_start = 0
    for a in a_list:
        step_batch.append(a - batch_start)
        batch_start = a + 1
    step_batch.append(n - batch_start + 1)

    result = 1
    for i, steps in enumerate(step_batch):
        result *= calc_step_combination(steps)
    print(result % 1000000007)


def main():
    n, m = map(int, input().split())
    a_list = []
    for i in range(0, m):
        a_list.append(int(input()))
    sol(n, a_list)


main()