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())
n += 1
a = [-1]
for i in range(m):
    a.append(int(input()))
a.append(n)

pattern = 0    
for i in range(1, len(a)):
#     print("for up to {}th step".format(a[i] - 1))
    step = [0] * (a[i] - a[i-1] - 1)
#     if a[i] - a[i-1] == 2:
#         step[1] = 1
#         for j in range(2, (a[i] - a[i-1])):
#             step[j] = step[j-1] + step[j-2]
#     else:
    step[1] = 1
    step[2] = 2
    for j in range(3, (a[i] - a[i-1] - 1)):
        step[j] = step[j-1] + step[j-2]
#     print(step)
#     print("there are {} patterns".format(max(step)))
    pattern += max(step)
print(pattern)