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)

implicit none
integer(8) :: l,r
integer(8),allocatable :: m(:)
integer(8) :: i,s

read *,l,r
allocate(m(l:min(r,l+2019)))
m(:) = 2019
do i = l,min(r,l+2019)
   m(i) = mod(i,2019)
enddo

i = minloc(m,DIM=1) + l - 1
s = m(i)
m(i) = 2019-1

write(*,'(i0)') mod(s * minval(m),2019)
end