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 l2019
  integer(8) :: l,r,lm,rm
  integer :: i,j,m

  read(*,*) l,r
  m=2020
  if((l/673).ne.(r/673)) then
     m=0
  else
     lm=mod(l,2019)
     rm=mod(r,2019)
     do	i=lm,rm-1
	do j=lm+1,rm
           if(mod(i*j,2019).lt.m) then
	      m=mod(i*j,2019)
	   endif
        enddo
     enddo
  endif
  write(*,'(i0)') m


end program l2019