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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*
 
fun main(args: Array<String>) {
    val argList = Scanner(System.`in`)
 
 
    val firstLine = argList.nextLine().split(" ")
    val l = firstLine[0].toLong()
    val r = firstLine[1].toLong()
 
    val e = RemainderMinimization2019()
    println(e.execute(l, r))
 
}
 
class RemainderMinimization2019 {
    private val r2019 = 2019
    fun execute(l: Long, r: Long): Long {
 
        val lMod = l % r2019
        val rMod = r % r2019
 
        if (lMod == 0L || rMod == 0L) return 0
 
        if (l + (r2019 - lMod)  <= r ) {
            // 2019以上離れている場合、
            // 2019の倍数を選べばよいので、modの最小値は0
            return 0
        }
 
        var ans: Long = 2018
        for (n in l..r) {
            for (i in n + 1..r) {
                val result = n * i % r2019
                if (ans > result) {
                    ans = result
                }
            }
        }
 
        return ans
    }
}