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: Accepted)

def mulmod(x,y,p):
    return x*y % p

def test(n):
    if n<1:
        return 1
    memo = [0]*(n+1)
    memo[0] = 1
    memo[1] = 1
    for i in range(2,n+1):
        memo[i] = (memo[i-1] + memo[i-2])%1000000007
    return memo[n]

n,m = map(int,input().split())
a =[]
pos = 0
result = 1
last = -1
for i in range(m):
    x = int(input())
    if (last+1) == x:
        print(0)
        exit(0)
    last = x
    a.append(x)

for i in a:
    result = mulmod(test(i-pos-1),result,1000000007)
    pos = i+1
 
result = mulmod(test(n-pos),result,1000000007)
print(result)