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: Wrong Answer)

import sys
N, M = map(int, input().split())

def fib(n):
    dp_list = [0] * n
    dp_list[0] = 1
    if n == 1:
        return 1
    dp_list[1] = 2
    
    for i in range(2, n):
        dp_list[i] = dp_list[i - 1] + dp_list[i - 2]
    return dp_list[n - 1]

if M == 0:
    print(fib(N))
    sys.exit()

a_list = [0] * M

for m in range(M):
    a_list[m] = int(input())

for m in range(M - 1):
    if a_list[m] + 1 == a_list[m + 1]:
        print(0)
        sys.exit()
    else:
        continue

range_list = [i for i in range(1, N + 1)]
new_list = [0] * (M + 1)


new_list[0] = [0] + range_list[0: a_list[0] - 1]
new_list[M] = range_list[a_list[M - 1]:]

if M - 1 >= 1:
    for m in range(1, M):
        new_list[m] = range_list[a_list[m - 1]: a_list[m] - 1]

MOD = 1000000007


count = 1
for item in new_list:
    if not item or len(item) == 1:
        continue
    else:
        count *= (fib(len(item) - 1) % MOD)
        count %= MOD
        #print(count)
print(count)