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)

#![allow(non_snake_case)]
#![allow(unused_imports)]
use proconio::input;
use std::cmp::max;
use std::cmp::min;
use std::collections::HashMap;
use std::collections::VecDeque;

fn main() {
    input! {
        L: i64,
        R: i64,
    }

    const MOD: i64 = 2019;

    // 0 * X = 0 (MOD p)
    if L == 0 {
        println!("0");
        return;
    }

    // 2019 * X = 0 (MOD p)
    if R - L >= MOD {
        println!("0");
        return;
    }

    // ここは2019 ** 2の探索でOK
    let mut ans = std::i64::MAX;
    for i in L..=R {
        for j in i + 1..=R {
            let cand = (i * j) % MOD;
            ans = min(ans, cand);
        }
    }

    println!("{}", ans);
}