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 Rust (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

use proconio::input;

fn main() {
    input! {
        l: u32,
        r: u32,
    }

    let mut ans = 2020;
    'outer: for i in l..r.min(l + 2019) {
        for j in l + 1..(r + 1).min(l + 2019) {
            ans = ans.min(((i % 2019) * (j % 2019)) % 2019);
            if ans == 0 {
                break 'outer;
            }
        }
    }
    println!("{}", ans);
}