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)

main :: IO ()
main = do
  [l,r] <- map (read :: String -> Int) . words <$> getLine
  let r_ = mod r 2019
  let l_ = r_ - ((mod r 2019) - (mod l 2019))
  if r-l < 2019 then print (ans l_ r_) else print 0
 
ans :: Int -> Int -> Int
ans m n = minimum [mod (i*j) 2019 | i <- [m..n], j <- [m..n], i < j]