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 abc133c

   implicit none

   integer(8) :: L, R, i, j , skip
   integer :: ans, calc_mod

   read(*,*) L, R

   ans = 2018
   R = min(R, L+673)

   do i = L, R-1
      do j =i+1, R

         calc_mod = mod(i*j,2019)
         if (ans > calc_mod ) then
            ans = calc_mod
            !if (ans == 0) goto 999  ! 0になったら打ち切る
         else
            cycle
         end if
      enddo
   enddo
999 continue

   print *, ans


end program abc133c