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 ccc

implicit none
integer(16) :: n, m, i, j, k, st
integer(16) :: one, two, thr, x, y, z, co, rs
integer(16),allocatable,dimension(:) :: a

read*, n, m
allocate(a(m+2))
do i=2,m+1
read*, a(i)
end do
a(1)=-1
a(m+2)=n+1
rs=1

do i=1,m+1
st=a(i+1)-a(i)-2
if(st<0) then
rs=0
exit
end if
co=0
do j=0,st/2
 one=st-2*j
 two=j
 thr=one+two
 x=1
 y=1
 z=1
  do k=1, one
  x=x*k
  end do
  do k=1,two
  y=y*k
  end do
  do k=1,thr
  z=z*k
  end do
  co=co+z/(x*y)
 end do
 rs=mod((rs*co),1000000007)
end do
if(rs<0) rs=rs+1000000007
write(*,'(i0)') rs
end program