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 qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T

main :: IO ()
main = do
  (l : r : _) <- map unsafeSignedDecimal . T.words <$> T.getLine :: IO [Int]
  print $ f l r

f :: Int -> Int -> Int
f l r | p 673 && p 3 = 0
      | otherwise = (l * (l + 1)) `mod` 2019
  where
    p :: Int -> Bool
    p d = let (m, n) = l `divMod` d in n == 0 || m < r `div` d

unsafeSignedDecimal :: T.Text -> Int
unsafeSignedDecimal s = case T.signed T.decimal s of
  Right (n, _) -> n