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: Time Limit Exceeded)

import sys
import math

N, M = list(map(int, input().split()))
a_list = list()

pre_a = None
for _ in range(M):
    a = int(input())
    if pre_a is not None and a - pre_a < 2:
        print(0)
        sys.exit()
    pre_a = a
    a_list.append(a)

a_list.append(N + 1)
start_step = 0
end_step = 0
answer = 1
for a in a_list:
    p = 0
    end_step = a - 1
    diff = end_step - start_step
    for x in range(diff // 2 + 1):
        p += math.factorial(diff - x) // math.factorial(x) // math.factorial(diff - 2 * x)
    answer *= p
    start_step = a + 1

answer %= 1000000007
print(answer)