Problem:
Score : 300 points

Problem Statement

You are given two non-negative integers L and R.
We will choose two integers i and j such that L \leq i < j \leq R.
Find the minimum possible value of (i \times j) \mbox{ mod } 2019.

Constraints

All values in input are integers.

0 \leq L < R \leq 2 \times 10^9

Input

Input is given from Standard Input in the following format:

L R

Output

Print the minimum possible value of (i \times j) \mbox{ mod } 2019 when i and j are chosen under the given condition.

Sample Input 1

2020 2040

Sample Output 1

2

When (i, j) = (2020, 2021), (i \times j) \mbox{ mod } 2019 = 2.

Sample Input 2

4 5

Sample Output 2

20

We have only one choice: (i, j) = (4, 5).

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

program main
implicit none
integer(8) :: l, r, i, j, res

read(*,*) l, r
if( r - l .ge. 2019 ) then 
   write(*,'(i0)') 0
   stop
else
   res = 2018
   do i = l, r-1
      do j = i+1, r
         if( mod( mod(i,2019)*mod(j,2019), 2019 ) .le. res ) then
            res = mod( mod(i,2019)*mod(j,2019), 2019 )
         end if
      end do
   end do
   write(*,'(i0)') res
end if
end program main