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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

from collections import Counter
n, m = map(int, input().split())
l = []
a0 = 0
for i in range(m):
    a = int(input())
    if a - a0 == 0:
        print(0)
        exit()
    l.append(a - a0 - 1)
    a0 = a + 1
l.append(n - a0)
d = Counter(l)
key = list(d.keys())

def cmb(n, r):
    if r > n//2:
        r = n - r
    val = 1
    for i in range(r):
        val *= n - i
        val //= i + 1
    return val

ans = 1
for k in key:
    val = 0
    for i in range(k//2 + 1):
        val += cmb(k - i, i)
    ans *= val**d[k]
    ans %= 10**9 + 7
print(ans)