Problem:
Score : 400 points

Problem Statement

Akari has n kinds of flowers, one of each kind.

She is going to choose one or more of these flowers to make a bouquet.

However, she hates two numbers a and b, so the number of flowers in the bouquet cannot be a or b.

How many different bouquets are there that Akari can make?

Find the count modulo (10^9 + 7).

Here, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet.

Constraints

All values in input are integers.

2 \leq n \leq 10^9

1 \leq a < b \leq \textrm{min}(n, 2 \times 10^5)

Input

Input is given from Standard Input in the following format:

n a b

Output

Print the number of bouquets that Akari can make, modulo (10^9 + 7). (If there are no such bouquets, print 0.)

Sample Input 1

4 1 3

Sample Output 1

7

In this case, Akari can choose 2 or 4 flowers to make the bouquet.

There are 6 ways to choose 2 out of the 4 flowers, and 1 way to choose 4, so there are a total of 7 different bouquets that Akari can make.

Sample Input 2

1000000000 141421 173205

Sample Output 2

34076506

Print the count modulo (10^9 + 7).

Solution in Fortran (gfortran v4.8.4) (judge verdict: Runtime Error)

program main

  implicit none

  integer :: n, a, b
  integer, allocatable :: sumi(:)
  integer    :: i

  integer(8)   :: ans

  read(*,*) n, a, b
  allocate( sumi(n) )
  
  ans = 1 
  sumi = 0
  do i = 1, n
    ans = ans * int( i, kind=8 )
    sumi(i) = ans
  end do
  
  ans = 0 
  do i = 1, n
    if( i == a .or. i == b ) cycle 
    if( i == n ) then
      ans = ans + 1
    else
      ans = ans + int( sumi(n)/sumi(i)/sumi(i) )
    end if
  end do

  print*, mod( ans, ( 10*9 + 7 ) )

end program main