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 = [int(input()) for _ in range(m)]

dp = [-1 for _ in range(n + 1)]

def checker(s, g):
    if s > g:
        return 0
    elif s == g:
        return 1
    else:
        if dp[g - s] != -1:
            return dp[g - s]
        else:
            ret = checker(s + 1, g) + checker(s + 2, g)
            dp[g - s] = ret
            return ret

if m == 0:
    c = checker(0, n)
else:
    s = 0
    g = a[0] - 1
    if g - s > 0:
        c = checker(s, g)
    else:
        c = 1
    if m == 1:
        s = a[0] + 1
        g = n
    else:
        for i in range(1, m):
            if a[i - 1] + 1 == a[i]:
                c = 0
                break
            else:
                s = a[i - 1] + 1
                g = a[i] - 1
                if g - s > 0:
                    c *= checker(s, g)
                s = a[m - 1] + 1
                g = n
    if g - s > 0:
        c *= checker(s, g)

print(c % 1000000007)