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: Wrong Answer)

let rec for_fold a b v f = if a >= b then v else for_fold (a+1) b (f a v) f
let ans =
  Scanf.scanf "%d %d" @@ fun l r ->
  let l, r = l mod 2019, r mod 2019 in
  if l = 0 && r < l then 0 else
  for_fold l (r+1) max_int @@ fun i a ->
    for_fold (i+1) (r+1) a @@ fun j a -> min a (i * j mod 2019)
let () = Printf.printf "%d\n" ans