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 OCaml (4.02.3) (judge verdict: Accepted)

let () =
    let main () =
        let l, r = Scanf.sscanf (read_line ()) "%d %d" (fun l r -> l, r) in
        let rec loop_l li count_l acc =
            let rec loop_r rj count_r acc =
                if rj > r || count_r = 2019 then acc else
                    loop_r (rj + 1) (count_r + 1) (min acc ((li * rj) mod 2019))
            in
            if li = r || count_l = 2019 then acc else
                loop_l (li + 1) (count_l + 1) (loop_r (li + 1) 0 acc)
        in
        Printf.printf "%d\n" (loop_l l 0 2019)
    in
    main ()