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 8.8.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as BS
import Data.Maybe
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt = fromIntegral . fst . fromJust . BS.readInteger
readIntList = map readInt . BS.words

getIntList = readIntList <$> BS.getLine

sim l l' r m | l' > r = m
             | m == (-1) = sim l (l'+1) r m'
             | m' < m = sim l (l'+1) r m'
             | otherwise = sim l (l' + 1) r m
             where
              m' = (l * l') `mod` 2019

simulate l r m | l == r = m
               | otherwise = simulate (l+1) r m'
               where
                m' = sim l (l+1) r m

main = do
  [l, r] <- getIntList
  if r >= l + 2019
    then print 0
    else do
      let l' = l `mod` 2019
      let r' = r `mod` 2019
      let s | r' == l' + 1 = (r' * l') `mod` 2019
            | l' > r' = 0
            | otherwise = simulate l' r' (-1)
      print s