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)

import math
from functools import lru_cache

MOD = 1000000007


@lru_cache(None)
def fibo(x):
    if x <= 1:
        return 1
    return fibo(x - 2) + fibo(x - 1)


n, m = list(map(int, input().split(" ")))
a_list = [int(input()) for _ in range(m)]
ngs = [i in a_list for i in range(n)]
ngs.append(False)
for i in range(n):
    if ngs[i] and ngs[i + 1]:
        print(0)
        exit()
cnts = []
cnt = 0

for ng in ngs:
    if ng:
        cnts.append(cnt)
        cnt = 0
        continue
    cnt += 1
cnts.append(cnt)
ans = 1
for c in cnts:
    if c != 0:
        ans *= fibo(c - 1)
# print(ngs)
# print(cnts)
print(ans % MOD)