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 (2.7.6) (judge verdict: Runtime Error)

import numpy as np
N, M = map(int, input().split())

MOD = 1000000007
dp = np.zeros(N, dtype = int)
if M != 0:
    A = np.array([int(input()) for _ in range(M)], dtype = int)
    dp[A - 1] = -1

if dp[0] == -1 and dp[1] == -1:
    pass
elif dp[0] == -1:
    dp[1] = 1
elif dp[1] == -1:
    dp[0] = 1
else:
    dp[0] = 1
    dp[1] = 2


if N >= 3:
    for n in range(2, N):
        if dp[n] != -1:
            dp[n] = (max(dp[n-1], 0) + max(dp[n-2], 0)) % MOD

print (dp[-1])