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)

N, M = map(int, input().split())
A = [int(input()) for _ in range(M)]

for i in range(M - 1):
    if A[i] + 1 == A[i + 1]:
        print(0)
        exit()

MAX_N = int(1e5) + 10
memo = [0 for i in range(MAX_N + 10)]
memo[0] = 1
memo[1] = 1
memo[2] = 2
for i in range(3, MAX_N + 10):
    memo[i] = memo[i - 1] + memo[i - 2]

now = 0
ans = 1

for a in A:
    diff = a - now - 1
    ans *= memo[diff]
    ans %= int(1e9 + 7)
    now = a + 1

diff = N - now
ans *= memo[diff]
ans %= int(1e9 + 7)
print(ans)