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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
  implicit none
  integer i
  integer(8) N,M,loc,a,ans
  read(*, *) N,M
  loc = 0
  ans = 1
  do i = 1,M
    read(*, *) a 
    ans = ans*fibonacci(a-loc)
    do
      if (ans > 1000000007) then
        ans = ans-1000000007
      else
        exit
      end if
    end do
    loc = a+1
  end do
  write(* ,*) mod(ans*fibonacci(N-loc+1),1000000007)

  stop
contains


  integer(8) function fibonacci(n)
    implicit none
    integer(8) xn, xn1, xn2, n, i
    if (n == 0) then
      xn = 0
    else if (n == 1) then
      xn = 1
    else
      xn2 = 0
      xn1 = 1
      do i = 2,n
        xn = xn1 + xn2
        xn2 = xn1
        xn1 = xn
      end do
    end if
    fibonacci = xn
    return
  end function fibonacci
  
end program main