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 (1.3.71) (judge verdict: Accepted)

fun main() {
  val (L, R) = readInts()
  val l = L
  val r = minOf(L + 2019, R)
  var min = Long.MAX_VALUE
  for (i in l until r) {
    for (j in (i + 1)..r) {
      min = minOf(min, (i.toLong() * j) % 2019)
    }
  }
  println(min)
}

fun gcd(a: Int, b: Int): Int = if (a < b) gcd(b, a) else if (b == 0) a else gcd(b, a % b)
fun gcd(a: Long, b: Long): Long = if (a < b) gcd(b, a) else if (b == 0L) a else gcd(b, a % b)
fun lcm(a: Int, b: Int): Int = (a * b) / gcd(a, b)
fun lcm(a: Long, b: Long): Long = (a * b) / gcd(a, b)

fun readString() = readLine()!!
fun readStrings() = readLine()!!.split(" ")
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readInts() = readLine()!!.split(" ").map { it.toInt() }
fun readLongs() = readLine()!!.split(" ").map { it.toLong() }

fun myBinarySearch(begin: Int, end: Int, isOk: (key: Int) -> Boolean): Int {
  var ng = begin
  var ok = end

  while (Math.abs(ok - ng) > 1) {
    val mid = (ok + ng) / 2
    if (isOk(mid)) {
      ok = mid
    } else {
      ng = mid
    }
  }

  return ok
}

fun <T> List<T>.myBinarySearch(isOk: (T) -> Boolean): Int {
  return myBinarySearch(-1, size) { index -> isOk(get(index)) }
}

fun <T> Array<T>.myBinarySearch(isOk: (T) -> Boolean): Int {
  return myBinarySearch(-1, size) { index -> isOk(get(index)) }
}