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 Data.Maybe
import Control.Monad
import qualified Data.ByteString.Char8 as C

readInteger' = fst.fromJust.C.readInteger
readLnInteger = map readInteger'.C.words<$>C.getLine
readCsInteger n = concat<$>replicateM n readLnInteger

x ? (a,b) = if x then a else b
half = flip div 2
aliq = ((0==).).mod

main = do
 [l,r] <- readLnInteger
 print $ solve [l,r]

solve [l,r] = minimum' 2019 [mod (i*j) 2019 | i <- [l..r], j <- [l..r], i<j]

minimum' t (a:x) = (null x)?(ans, minimum' ans x) where
  ans = (t<a)?(t,a)