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: Time Limit Exceeded)

program main
integer(16) :: l,r,i,j,m,mo,tmp,a
m=2019
read(*,*)l,r

do i = l,r
if (mod(i,2019)==0) then
m = 0
endif
end do

l = mod(l,2019)
r = mod(r,2019)
!if (r < l) then
!tmp = r
!r = l
!l = tmp
!end if

if (l /= r) then
do i = l,r-1
do j = i+1,r
mo = mod(i*j,2019)
if (m > mo) m = mo
end do
end do
write(*,*)m

else
write(*,*)l
end if

end program main