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 (1.6) (judge verdict: Accepted)

// 参考: https://atcoder.jp/contests/abc133/submissions/6278434
// matsuu さんありがとうございました。

package main

import (
	"fmt"
)

func minimumRemainder(minNum int, maxNum int, modNumInit int) int {
	// 各余り値の最小値
	// (最初なので考えられる余り値の最大値)
	var modNum int = modNumInit

	// minNum(i)がmaxNumに徐々に接近！
	for i := minNum; i < maxNum; i++ {
		// i+1(j)がmaxNumに徐々に接近してくっつく！
		for j := i + 1; j <= maxNum; j++ {
			// 現在のminNum(i)×(i+1...maxNum) ÷ 2019 の余り値
			remainder := (i * j) % modNumInit
			// 現在の最小値より小さかったら
			if remainder < modNum {
				// 最小値更新
				modNum = remainder
				// 余りが0になった時点で最小値が決定したので処理終了
				if modNum == 0 {
					return modNum
				}
			}
		}
	}
	return modNum
}

func main() {
	var minNum, maxNum int
	fmt.Scan(&minNum, &maxNum)
	fmt.Println(minimumRemainder(minNum, maxNum, 2019))
}