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)

def fib2(n):
    if n <= 1:
        return n
    result = [1, 0, 0, 1]
    matrix = [1, 1, 1, 0]
    while n > 0:
        if n % 2:
            result = mul(matrix, result)
        matrix = mul(matrix, matrix)
        n //= 2
    return result[2]

def mul(a, b):
    return [a[0]*b[0] + a[1]*b[2],
            a[0]*b[1] + a[1]*b[3],
            a[2]*b[0] + a[3]*b[2],
            a[2]*b[1] + a[3]*b[3]]

inp = input()
n = int(inp.split()[0])
m = int(inp.split()[1])
a = []
for i in range(m):
  a.append(int(input()))
  
mul_list = []
nochance = False
for j in range(m+1):
  if j == 0:
    ss = a[0]
    if ss <= 0:
      p = 1
    else:
      p = fib2(ss)
    mul_list.append(p)
  elif j == m:
    step = n - a[-1]
    p = fib2(step)
    mul_list.append(p)
  else:
    step = a[j] - a[j-1] - 1
    if step == 0:
      nochance = True
      break
    p = fib2(step)
    mul_list.append(p)
    

if nochance:
  print(0)
else:
  ans = 1
  for b in mul_list:
    ans *= b
  print(ans%1000000007)