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: Runtime Error)

def fiv(n):
    return (((1+(5)**(1/2))/2)** (n + 1) - ((1-(5)**(1/2))/2)** (n + 1))/(5**(1/2))

n, m = map(int, input().split())
broken = []
for i in range(m):
	broken.extend(map(int, input()))

p = [0] * (m + 1) #broken間の登り方list

for i in range(m + 1):
    if i == 0: #a1 さいしょ
        if broken[0] == 1:
            p[0] = 1
        else:
            p[0] = fiv(broken[0] - 1)
    if i == m: #am さいご
        if broken[m - 1] == n - 1:
            p[m] = 1
        else:
            p[m] = fiv(n - broken[0] - 1)
    
    else:
        if broken[i] - broken[i - 1] - 1 == 0:
            print('0')
            exit()
        else:
            p[i] = fiv(broken[i] - broken[i - 1] - 1)

ans = 1
for i in range(m + 1):
    ans = ans * p[i] / 1000000007

print(ans)