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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local l, r = io.read("*n", "*n")
if 2020 < r - l then
  print(0)
else
  local ret = 2018
  local mmi = math.min
  for i = l, r - 1 do
    for j = i + 1, r do
      ret = mmi(ret, (i * j) % 2019)
    end
  end
  print(ret)
end