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)

N,M=map(int,input().split())
A=[int(input()) for i in range(M)] #0からM-1まで


root=[0]*(N+2)   #間がiの時の行き方
for i in range(N+2):    #0からN-1まで
    if i==0:
        root[0]=0
    elif i==1:
        root[1]=1
    elif i==2:
        root[2]=1
    else:
        root[i]=root[i-1]+root[i-2]
#print(root)

ans=0
if M==0:
    print(root[N+1])
    exit()

for i in range(M+1): #0からM
    if i==0:
        ans=root[A[0]]
    elif i==M:
        ans*=root[N-A[M-1]]
    else:
        ans*=root[A[i]-A[i-1]-1]
print(ans%1000000007)