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: Time Limit Exceeded)

import re
from operator import mul
from functools import reduce


def cmb(n, r):
    r = min(n-r, r)
    if r == 0:
        return 1
    numerator = reduce(mul, range(n, n - r, -1))
    denominator = reduce(mul, range(1, r + 1))
    return numerator // denominator


def Step(num):
    ans = 0
    for i in range(num//2 + 1):
        ans += cmb(num-i, i)
    return ans


N, M = map(int, input().split())
a = [int(input()) for _ in range(M)]

if M > 0:
    step = ['1' for _ in range(N)]
    for i in range(M-1):
        if a[i]+1 == a[i+1]:
            print(0)
            exit()
        else:
            step[a[i]-1] = step[a[i]] = '2'
    step[a[M-1]-1] = step[a[M-1]] = '2'
elif M == 0:
    print(Step(N) % 1000000007)
    exit()

one_one = list(map(len, re.findall(r'1+', ''.join(step))))
ans = 1
for i in one_one:
    ans *= Step(i)

print(ans % 1000000007)