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 remainder_minimization_2019
    implicit none
    integer(8):: l,r,c,i,j
    integer(8),parameter:: max_loop=2019
    c=2019
    read*,l,r
    do i=l, min(r,l+max_loop)-1
        do j=i+1,min(r,l+max_loop)
            c = min(c,mod(i*j,2019))
        end do
    end do
    print*, c
        
end program remainder_minimization_2019