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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mce, mfl, msq, mmi, mma = math.ceil, math.floor, math.sqrt, math.min, math.max
local l, r = io.read("*n", "*n")

local ret = 2019
local imax = mmi(l + 2018, r - 1)
for i = l, imax do
  local jmax = mmi(i + 1 + 2018, r)
  for j = i + 1, jmax do
    local cand = ((i % 2019) * (j % 2019)) % 2019
    ret = mmi(ret, cand)
  end
end
print(ret)