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: Time Limit Exceeded)

import           Control.Monad
import qualified Data.Array.IO               as IO
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

main = do
  [l, r] <- getIntList
  let r'= min (r + 2020) r

  res <- VM.new 1
  VM.write res 0 (10^9 :: Int)

  forM_ [l..(r-1)] $ \x ->
    forM_ [(l+1)..r] $ \y -> do
      t <- VM.read res 0
      VM.write res 0 (min t (x * y `mod` 2019))

  ans <- VM.read res 0
  print ans