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: Runtime Error)

program main
 integer(16) n,m,i,p
 integer(16), allocatable :: a(:),pat(:)
 
 p=0
 read(*,*) n,m
 if(m==0)then
  p=-1
 end if
 
 if(p==0)then
  allocate(a(1:m),pat(1:n+2))
  read(*,*) a
  do i=1,n
   pat(i)=0
  end do
 
  pat(a(1)+1)=-1
  do i=2,m
   if(a(i)==a(i-1)+1)then
    p=-1
    exit
   end if
   pat(a(i)+1) = -1
  end do
  
  pat(1)=1
  if(p==0)then
   do i=1,n
    if(pat(i)/=-1)then
     if(pat(i+1)/=-1)then
      pat(i+1)=mod(pat(i+1)+pat(i),1000000007)
     end if
     if(pat(i+2)/=-1)then
      pat(i+2)=mod(pat(i+2)+pat(i),1000000007)
     end if
    end if
   end do
  end if
 end if
 
 write(*,*) pat(n+1)
end program main