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 (GNU Fortran 9.2.1) (judge verdict: Accepted)

      PROGRAM TypicalStairs
      IMPLICIT NONE
      integer(16) :: n,m,a(10**5)
      integer(16) :: i,pattern(-1:10**5),aCnt=1
      
      read*,n,m
      do i = 1,m
        read*,a(i)
      end do
      
      pattern = 0
      !i=1
      if( a(aCnt)==1 )then
        pattern(1) = 0
        aCnt = aCnt + 1
      else
        pattern(1) = 1
      end if
      
      !i=2
      if( a(aCnt)==2 )then
        pattern(2) = 0
        aCnt = aCnt + 1
      else
        pattern(2) = pattern(1) + 1
      end if
      
      do i = 3,n
        if( a(aCnt)==i )then
          pattern(i) = 0
          aCnt = aCnt + 1
        else
          pattern(i) = pattern(i-2) + pattern(i-1)
          pattern(i) = mod(pattern(i),10**9+7)
        end if
      end do
      
      print*,pattern(n)
  !    print*,pattern(1:n)
      
      
      
      
      END PROGRAM