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)

n, m = map(int, input().split())
a = []
for _ in range(m):
    _a = int(input())
    try:
        if _a == a[-1]:
            continue
    except:
        pass
    a.append(_a)
a.append(n + 1)
m = len(a)

memo = {0: 1, 1: 1, 2: 2}
def chk(n):
    if n in memo:
        return memo[n]
    else:
        make(n)
        return memo[n]

def make(n):
    if n in memo:
        return
    make(n - 1)
    make(n - 2)
    memo[n] = (memo[n-1] + memo[n-2]) % 1000000007

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

cur = 0
tot = 1
#from sys import stderr
#for k in range(100):
#    print(f'0-{k}: {chk(k)}', file=stderr)

for i in range(m):
    nxt = a[i] - 1
    add = chk(nxt - cur)
    #print(f'{cur}-{nxt}: {add}', file=stderr)
    tot *= add
    tot %= 1000000007
    cur = nxt + 2
print(tot % 1000000007)