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 Python (3.4.3) (judge verdict: Accepted)

import itertools

l, r = map(int, input().split())
l_rest = l % 2019
r_rest = r % 2019

if l_rest == 0 or r_rest == 0:
    print(0)
elif r-l < 2019:
    lr_list = list(range(l_rest, r_rest+1))
    lr_comb = list(itertools.combinations(lr_list, 2))
    min_rest = 2018
    for comb in lr_comb:
        rest = comb[0] * comb[1]
        min_rest = min(min_rest, rest%2019)
    print(min_rest)
elif r-l >= 2019:
    print(0)