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)

#動的計画法(DP)
#ブログ「けんちょんの競プロ精進記録」参考
#URL: https://drken1215.hatenablog.com/entry/2019/06/10/140000


N,M = map(int,input().split())
MOD = 1000000007
issafe = [True]*N # issafe[v]: v段目が壊れていないかどうか

for _ in range(M):
    i = int(input())
    issafe[i] = False # i 段目は壊れている

#DPテーブル
dp = [0]*(N+1)

#初期条件
dp[0] = 1
if issafe[1]:dp[1] = 1

#ループ
for n in range(2,N+1):
    if issafe[n-1]: dp[n] += dp[n-1]
    if issafe[n-2]: dp[n] += dp[n-2]
    dp[n] %= MOD

print(dp[N])