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 qualified Data.ByteString.Char8 as BS
import Data.Char
import Data.List

toInts :: IO [Int]
toInts = unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

trunc :: Int -> Int -> (Int, Int)
trunc l r =
  if l - r <= 2018
    then (l, r)
    else (l, l + (mod (r - l) 2019))

solver :: Int -> Int -> Int
solver l r =
  if l - r > 2018
    then 0
    else let (l_, r_) = trunc l r
          in minimum [mod (i * j) 2019 | i <- [l_ .. r_], j <- [(i + 1) .. r_]]

main :: IO ()
main = do
  l:r:[] <- toInts
  print $ solver l r