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)

#c
n,m = map(int,input().split())
a=[]
for i in range(m):
    a.append(int(input()) )
mod=10**9 + 7

def cmb(n, r, m,g1,g2):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % m

def nCrMOD(n,r,m):
    g1 = [1, 1]
    g2 = [1, 1]
    inverse = [0, 1]
    for i in range( 2, n + 1 ):
        g1.append( ( g1[-1] * i ) % m )
        inverse.append( ( -inverse[m % i] * (m//i) ) % m )
        g2.append( (g2[-1] * inverse[-1]) % m )
    return cmb(n,r,m,g1,g2)


c=0
for i in range(m-1):
    if a[i]==a[i+1]-1: c+=1
if c!=0:
    print(0)
elif m==0:
     print( sum( nCrMOD(n-i,i,mod) for i in range(n//2+1) )%mod )
    
    
else:
    b=[a[0]-1] + [a[j+1]-a[j]-2 for j in range(m-1)] + [n-a[-1]-1]
    cc=[ sum( nCrMOD(bb-i,i,mod) for i in range(bb//2+1) )%mod for bb in b ]

    ans=1
    for ccc in cc:
        ans = ans*ccc%mod
    print(ans)