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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Control.Applicative
import Data.List

solve _ m1 0 = [m1, 0]
solve _ 0 m2 = [0, m2]
solve [] m1 m2 = [m1, m2]
solve (x:xs) m1 m2 = do
  let x' =  x `mod` 2019
  let (m1':m2':_) = sort [m1, m2, x']
  solve xs m1' m2'

main = do
  [l, r] <- (map read).words <$> getLine :: IO [Int]
  let xs = [l..r]
  print $ (`mod` 2019) $ product $ solve (drop 2 xs) ((xs !! 0) `mod` 2019) ((xs !! 1) `mod` 2019)