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)

# -*- coding: utf-8 -*-
n, m = map(int, input().split())
BIGNUM = 10 ** 9 + 7

if m > 0:
    last_ana = int(input())
    blocks = [last_ana]

    for _ in range(1, m):
        ana = int(input())
        blocks.append(ana - last_ana - 1)
        last_ana = ana
    blocks.append(n - last_ana)
else:
    blocks = [n + 1]

if 0 in blocks:
    ans = 0
else:
    b_max = max(blocks)
    c = [1, 1]
    for i in range(2, b_max):
        ctmp = c[i - 1] + c[i - 2]
        c.append(ctmp % BIGNUM)

    ans = 1
    for num in blocks:
        if num == 1:
            continue
        ans = (ans * c[num - 1]) % BIGNUM
        if ans == 0:
            break

print(ans)