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: Wrong Answer)

L, R = gets.chomp.split(" ").map(&:to_i)
MOD = 2019
MOD2 = 673
MOD3 = 3

ans = 0
if (R - L) < (MOD - 1) && (L % MOD) < (R % MOD) then
  if ((R - L) > (MOD2 - 1) || (L % MOD2) >= (R % MOD2)) && ((R - L) > (MOD3 - 1) || (L % MOD3) >= (R % MOD3)) then
    # 3 * 673 = 2019
    ans = 0
  else
    s = [L % MOD, (R % MOD) + MOD].min
    ans = (s * (s + 1)) % MOD
  end
end

puts ans