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

def cul_1to2(i):
	global ppre_step
	global pre_step
	global now_step
	if i == 1:
		if i not in denger_list:
			ppre_step,pre_step,now_step = pre_step,0,1

		if i in denger_list:
			ppre_step,pre_step,now_step = pre_step ,0,0

	if i == 2:
		if i not in denger_list:
			if 1 in denger_list:
				ppre_step,pre_step,now_step = pre_step,now_step,1	
			else:
				ppre_step,pre_step,now_step = pre_step,now_step,2
		if i in denger_list:
			ppre_step,pre_step,now_step = pre_step ,now_step,0

	return ppre_step,pre_step,now_step


N,M = map(int,input().split())
step_list = list(range(N+1))
denger_list = list()
Int_pre =None
for i in range(M):
	if Int_pre != None:
		Int = int(input())
		if abs(Int - Int_pre) == 1:
			print(0)
			sys.exit()
		else:
			denger_list.append(Int)
			Int_pre = Int
	else:
		Int = int(input())
		denger_list.append(Int)
		Int_pre = Int

ppre_step = None
pre_step  = None
now_step  = 0

for i in range(N+1):
	if i == 0:
		continue

	if i <= 2:
		cul_1to2(i)
	
	else:

		if i not in denger_list:
			ppre_step = pre_step
			pre_step  = now_step
			now_step  = ppre_step + pre_step

		elif i in denger_list:
			ppre_step = pre_step
			pre_step  = now_step
			now_step  = 0 




print(now_step%1000000007)