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)

n, m = map(int, input().split())
now_step = 0
# count=1*a+2*bとなるような、0以上の全てのa,bについて、1をa個、2をb個並べる並べ方を返す.
# [1,(a+b)]からa個を選ぶ選び方と同じ
# ただし、これはnumber-1とnumber-2が分かっている場合は、number-1から1つ、あるいはnumber-2から二つ進む進み方の和で表せる
# よって、counte_steps(number) = count_steps(number-1) + count_steps(number-2)
# 初期値はcount_steps(1) = 1, count_steps(2) = 2,count_steps(0) = 0
checked_steps = {-1:0, 0:1, 1:1, 2:2}
divide_num = 1000000007 

for i in range(3, n):
    checked_steps[i] = (checked_steps[i-1] + checked_steps[i-2]) % divide_num

all_count = 1
for i in range(m):
    a = int(input())
    all_count = (all_count * checked_steps[a - 1 - now_step]) % divide_num
    now_step = a + 1
all_count = (all_count * checked_steps[n - now_step]) % divide_num
print(all_count % divide_num)