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)

import sys

[N, M] = [int(i) for i in input().split()]

steps = [0, 1, 2]
for i in range(3, N+1):
    steps.append(steps[i-1] + steps[i-2])
  
if M == 0:
    print(steps[N] % 1000000007)
    sys.exit()
    
As = []
for i in range(M):
    As.append(int(input()))
    
deffs = []

if As[0] != 1:
    deffs.append(As[0] - 1)
else:
    deffs.append(1)

for i in range(1, M):
    d = As[i] - As[i-1] -2
    if d == 0:
        deffs.append(1)
    elif d == -1:
        deffs.append(0)
    else:
        deffs.append(d)

if N - As[M-1] - 1 != 0:
    deffs.append(N - As[M-1] - 1)
else:
    deffs.append(1)

ans = 1

for i in range(len(deffs)):
    ans *= steps[deffs[i]]
    
print(ans % 1000000007)