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)

n, m = map(int, input().split())
MOD = 1000000007

fact=[0,1]
fact_inv=[0]*(n+1)
for i in range(2,n+1):
  fact.append(fact[-1]*i % MOD)

fact_inv[n] = pow(fact[n],MOD-2,MOD)
for i in range(n-1,-1,-1):
  fact_inv[i] = fact_inv[i+1]*(i+1)%MOD

def comb(n,r):
  return fact[n]*fact_inv[r]*fact_inv[n-r]%MOD

def sigmaComb(dis):
  ans=0
  if dis == 1 or dis == 0:
    return 1
  end=dis//2 if dis%2 != 0 else dis//2+1
  for i in range(end):
    t=comb(dis-i,i)
    ans+=t
  return ans

hole=[0]
ans=1
for i in range(m):
  t = int(input())
  availLeft=hole[-1]
  availRight=t-1
  dis=availRight-availLeft
  if dis <0:
    ans=0
    break

  ans=ans*sigmaComb(dis)%MOD
  # print("dis=",dis,t,ans)
  hole.append(t+1)
else:
  availLeft=hole[-1]
  availRight=n
  dis=availRight-availLeft
  #print("dis=",dis,hole[-1],ans)
  ans=ans*sigmaComb(dis)%MOD

print(ans%MOD)