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())
now = 0
count = 1
flag = True
for _ in range(M):
        a = int(input())
        if a == now:
                print(0)
                flag = False
                break
        else:
                dif = a - now - 1
                x = int(dif / 2)
                y = 0
                for i in range(x+1):
                        z = 1
                        j = dif - 2*i
                        for k in range(i):
                                z *= (i+j-k)/(i-k)
                        y += z
                count *= y
                count = count % 1000000007
                now = a + 1
if flag:
        dif = N - now
        x = int(dif/2)
        y = 0
        for i in range(x+1):
                z = 1
                j = dif - 2*i
                for k in range(i):
                        z *= (i+j-k)/(i-k)
                y += z
        count *= y
        print(int(count%1000000007))