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)

import math
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

N, M = map(int, input().split())

sl = []
cnt = -1
for i in range(M):
    a = int(input())
    b = (a - 1) - (cnt + 1)
    if b == -1:
        print(0)
        break
    sl.append(max(b, 1))
    cnt = a
else:
    sl.append(max(N - (a + 1), 1))
    ans = 1
    for s in sl:
        p = 0
        for i in range(s):
            j = s - i
            if (i <= j):
                p += combinations_count(j, i)
            else:
                break
        ans *= p
        ans = ans % 1000000007
    print(ans % 1000000007)