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 min
  implicit none
  integer(8) :: l, r, lmod, ans, rmod, i, j
  integer(8),parameter :: a = 2019
  
  read *, l, r 
  lmod = mod(l,a)
  rmod = mod(r,a)
  if (r >= (l/a+1)*a) then
    ans = 0
  else 
    do i = l, r 
      do j = i+1, r
        if (mod(i*j,a) < ans) ans = mod(i*j,a)
      end do
    end do
  end if
  print '(i0)', ans
  stop
end program min