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: Accepted)

# https://atcoder.jp/contests/abc129/tasks/abc129_c
# 典型的なDP


from copy import deepcopy


def full(shape, full_value):
    if isinstance(shape, tuple):
        if len(shape) == 2:
            return [[full_value] * shape[1] for _ in range(shape[0])]
        else:
            import numpy as np
            return np.full(shape, full_value).tolist()
    else:
        return [full_value] * shape


MOD = 10**9 + 7
# dp[i]をi段目までの通りの数とする。
N, M = list(map(int, input().split()))
to_zero = full((N + 1), False)
for _ in range(M):
    to_zero[int(input())] = True  # 床が抜けているところ

# dpテーブルの用意
dp = full((N + 1), -1)
dp[0] = 1
dp[1] = 0 if to_zero[1] else 1
for i in range(2, N + 1):
    dp[i] = 0 if to_zero[i] else dp[i - 2] + dp[i - 1]
    if dp[i] > MOD:
        dp[i] %= MOD

print(dp[-1])