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: Wrong Answer)

program ccc

implicit none
integer(8) :: l, r, i, one, two

read*, l, r

do i=1,10000
if(l>=2019) then
l=l-2019
r=r-2019
else
exit
end if
end do

if(r>=2019) then
write(*,'(i0)') 0
return
end if

one=mod(l*(l+1),2019)
two=mod(r*(r-1),2019)

write(*,'(i0)') min(one,two)

end program