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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const L = parseInt(arg[0].split(" ")[0]);
    const R = parseInt(arg[0].split(" ")[1]);
    
    if(R - L + 1 >= 2019) {
        // 2つの数の差が2019以上のとき、必ず2019の倍数が存在するので0
        console.log(0);
    } else {
        const Lmod = L % 2019;
        const Rmod = R % 2019;
        
        let min = Infinity;
        
        for(let i=Lmod; i<Rmod; i++) {
            for(let k=parseInt(i)+1; k<=Rmod; k++) {
                min = Math.min((i * k) % 2019, min);
            }
        }
        
        console.log(min);
    }
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));