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
input = sys.stdin.readline

mod=1000000007
n,m=map(int,input().split())
a=[]
for i in range(m):
    a.append(int(input()))
al=len(a)
if al>0:
    a.sort()

f=0
for i in a:
    if i+1 in a:
        f=1
        break
if f==1:
    print(0)
else:
    dp=[0]*(n+1)
    dp[0]=1
    if 1 in a:
        dp[1]=0
        a.pop(0)
        al-=1
    else:
        dp[1]=1
    
    for i in range(2,n+1):
        if al>0 and i==a[0]:
            dp[i]=0
            a.pop(0)
            al-=1
        else:
            dp[i]=dp[i-1]%mod+dp[i-2]%mod
    print(dp[n]%mod)