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())
a=[]
for i in range(m):
	a.append(int(input()))
if m>1:
	for i in range(m-1):
		if a[i]+1==a[i+1]:
			print(0)
			exit()
list1=[1,1]
for i in range(n):
	nu=list1[i]+list1[i+1]
	list1.append(nu)
ans=[]
x=a[0]
if x==1:
	ans.append(1)
else:
	ans.append(list1[x-1])
if m>1:
	for i in range(0,m-1):
		x=a[i+1]-a[i]-1
		ans.append(list1[x-1])
x=n-a[-1]
ans.append(list1[x-1])
import functools
import operator
result = functools.reduce(operator.mul, ans)
p,mod=divmod(result, 1000000007)
print(mod)