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)

n,m = map(int,input().split())
a = [int(input())-1 for i in range(m)]
dp = [0]*n
if n==1:
    if 0 in a:
        print(0)
        exit()
    else:
        print(1)
        exit()
if 0 in a:
    if 1 in a:
        print(0)
        exit()
    else:
        dp[0]=0
        dp[1]=1
else:
    if 1 in a:
        dp[0]=1
        dp[1]=0
    else:
        dp[0]=1
        dp[1]=2
for i in range(2,n):
    if i-1 in a and i-2 in a:
        print(0)
        exit()
    elif i-1 in a:
        dp[i]=dp[i-2]
    elif i-2 in a:
        dp[i]=dp[i-1]
    else:
        dp[i]= dp[i-1]+dp[i-2]
        if dp[i]>10**9+7:
            dp[i]-=(10**9+7)
print(dp[n-1])