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 (3.8.2) (judge verdict: Time Limit Exceeded)

N, M = map(int, input().split())
mae = 0
sub = []
flag = False

for _ in range(M):
  broken = int(input())
  if mae == broken: # 不可能
    flag = True
  if flag:
    continue
  if mae+1 == broken:
    mae = broken + 1
    continue
  sub.append(broken-1-mae)
  mae = broken + 1
# 無理な時
if flag:
  print(0)
  exit()
# forの中で最後まで行ってない分の追加
if mae != N:
  sub.append(N-mae)

from operator import mul
from functools import reduce

# nCrの関数
def C(n, r):
    r = min(r, n - r)
    numer = reduce(mul, range(n, n - r, -1), 1)
    denom = reduce(mul, range(1, r + 1), 1)
    return numer // denom
# 壊れてるやつの間の上り方の場合の数
def count(n):
  ans = 1
  for i in range(n//2):
    ans += C(n-i-1, i+1)
  return ans

ans = 1
waru = 10**9+7
for s in sub:
  ans *= count(s)%waru
print(ans%waru)