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())
MOD = 10**9 + 7
A = [int(input()) for _ in range(M)]
if M == 0:
    print(pat[N] % MOD)
else:
    pat = [0] * (N+1)
    pat[1] = 1
    pat[2] = 2
    for i in range(3, N+1):
        pat[i] = (pat[i-1] + pat[i-2]) % MOD
    steps = []
    if len(A) > 1
        for i in range(M-1):
            d = A[i+1] - A[i]
            if d > 2:
                steps.append(d-2)
            elif d == 1:
                steps.append(0)
    if A[0] != 1:
        steps = [A[0] - 1] + steps
    if A[-1] != N-1:
        steps += [N - A[-1] - 1]
    ans = 1
    for s in steps:
        ans = (ans * pat[s]) % MOD
    print(ans)