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 Go (1.14.1) (judge verdict: Accepted)

package main

import "fmt"

var moduler = 2019

func main() {
	var l, r int
	fmt.Scan(&l, &r)
	if r-l >= 2019 {
		fmt.Println(0)
		return
	}
	ans := l * (l + 1) % moduler
	for i := l; i < r; i++ {
		for j := l + 1; j <= r; j++ {
			mod := i * j % moduler
			if mod < ans {
				ans = mod
			}
		}
	}
	fmt.Println(ans)
}