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)

(declaim (optimize (speed 3) (debug 0) (safety 0)))
(let* ((n (read))
       (m (read))
       (ans 2019))
  (loop :named p-loop :for p :from n :upto (1- m)
        :do(loop :for q :from (1+ p) :upto m :do(if (= 0 (mod (* p q) 2019))
                                                    (progn (setf ans 0) (return-from p-loop))
                                                    (if (< (mod (* p q) 2019) ans)
                                                        (setf ans (mod (* p q) 2019))) )))
  (princ ans))