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 sys
n, m = map(int, input().split())
a_list = []
for i in range(m):
    a_i = int(input())
    a_list.append(a_i)
#print(n, m, a_list)
#print(a_list)
flag = 0

'''
def stepup(x):
    #x段
    ans = 0
    for i in range(x):
        if i==0:
            two_before=1
            ans=1
        elif i==1:
            one_before=2
            ans=2
        else:
            #print(two_before, one_before)
            ans = one_before+two_before
            two_before = one_before
            one_before = ans
    return(ans)
'''
def stepup(x):
    x += 1
    ans = ((1 + 5**0.5) / 2)**x / 5**0.5 + 0.5
    return(int(ans))

#print(stepup(1))
#print(a_list)
for i in range(m):
    if i==0:
        if a_list[i]==1:
            count = 1
            continue
        else:
            count = stepup(a_list[0]-1)
    else:
        if a_list[i]-a_list[i-1]==1:
            #print(a_list[i], a_list[i-1])
            flag = 1
            break
        elif a_list[i]-a_list[i-1]==2:
            pass
        else:
            #print(stepup(23))
            #print(i, stepup(a_list[i]-a_list[i-1]))
            count *= stepup(a_list[i]-a_list[i-1]-2)
    #print(count)
#print(len(a_list), m)
if n-a_list[m-1]==1:
    pass
else:
    count *= stepup(n-a_list[i]-1)
#print(count)

if flag==1:
    print(0)
else:
    print(count%1000000007)
#print((stepup(20)**4 * stepup(10))%1000000007)