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 >= 2018) then
    write (*, "(i0)") 0
  else
    res = 2019
    do i = l, r - 1
      do j = i + 1, r
        res = min(res, mod(i * j, 2019_8))
      end do
    end do
    write (*, "(i0)") res
  end if
end program main