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: Runtime Error)

N, M = map(int, input().split())
bre = []
flag = 0
A = []
for i in range(M):
    bre.append(int(input()))
#print(bre)
A.append(bre[0] - 1)
count = 0
if len(bre) >= 2:
    for i in range(len(bre) - 1):
        a = bre[i + 1] - bre[i]
        A.append(a - 2)
        if a == 1:
            #print(0)
            flag = 1
A.append(N - bre[len(bre) - 1] - 1)

if flag == 0:
    suu = [0, 1, 2]
    for i in range(2, max(A)):
        suu.append(suu[i] + suu[i-1] )
    #print(suu)
    for i in A:
        if count == 0:
            count = suu[i]
        else :
            count *= suu[i]
    print(count % 1000000007)