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 Ruby (2.3.3) (judge verdict: Accepted)

L,R = gets.chomp.split(" ").map(&:to_i)
L_diff = L % 2019
R_diff = R % 2019


if (R<2019)
    mods = []
    L.upto(R-1) do |i|
        (i+1).upto(R) do |j|
            mods << (i*j)%2019
        end
    end
    puts mods.min
elsif (L>2019)
    if (L/2019) != (R/2019)
        puts 0
    else
        mods = []
        L_diff.upto(2019) do |i|
            (i+1).upto(R_diff) do |j|
                mods << (i*j)%2019
            end
        end
        puts mods.min
    end
elsif (R>2019)&&(L<2019)
    puts 0
elsif (R==2019)||(L==2019)
    puts 0
end