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: Accepted)

import Data.Bits
import Data.List
import Control.Monad
import qualified Data.Vector.Unboxed as V
import Control.Monad.ST
import Data.Maybe (fromMaybe)
import qualified Data.ByteString.Lazy.Char8 as B
import Debug.Trace

check :: [Int] -> [Int] -> Bool
check xs ys = (foldl (\x (y,y') -> x + (y-y')^2) 0 (zip xs ys)) == (((^2) . floor . sqrt . fromIntegral) $ foldl (\x (y,y') -> x + (y-y')^2) 0 (zip xs ys))

main :: IO ()
main = do
  [l,r] <- map read.words <$> getLine :: IO [Int]
  if r-l > 2019 then print 0
    else print $ minimum [ (i*j) `mod` 2019 | i <- [l,l+1..r], j <- [l,l+1..r], i < j]