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 Scala (2.11.7) (judge verdict: Accepted)

import scala.io.{StdIn => in}

object Main extends App {
  val mod = 2019L
  val Array(l, r) = in.readLine.split(" ").map(_.toLong)

  var res = Int.MaxValue + 1L
  for{
    i <- 0L until mod
    if l + i < r
    j <- (i + 1L) until (i + 1L + mod)
    if l + j <= r
  } {
    val v = ((l+i) % mod) * ((l+j) % mod) % mod
    if(res > v) res = v
  }

  val ans = res
  println(ans)
}