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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun solve (l r)
  (loop for i from l below r
        minimize
        (loop for j from (1+ i) to r
              for x = (mod (* i j) 2019)
              when (= x 0)
              do (return-from solve 0)
              minimize x)))
(princ (solve (read) (read)))