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)

N, M = map(int, input().split())
mod = 10**9 + 7
a = [int(input()) for _ in range(M)]

b = [0] * N
b[0] = 1
b[1] = 2
for i in range(2, N):
    b[i] = b[i-1] + b[i-2]
b = [1] + b


for i in range(M-1):
    if a[i] + 1 == a[i+1]:
        print(0)
        quit()


a = [0] + a
if M == 0:
    ans = b[N]
    print(ans)
    quit()
else:
    ans = b[a[1] - a[0] -1]
for i in range(2, M+1):
    ans *= b[a[i]-1 - a[i-1]- 1]

ans *= b[N - a[M] -1]
print(ans % mod)