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)

(let ((L (read))
      (R (read))
      (arr (make-array 0 :element-type 'integer
                         :adjustable t
                         :fill-pointer 0))
      (ans 10000))
     (loop for i from L upto (min R (+ L 4040))
           do (vector-push-extend (rem i 2019) arr))
     (setf arr (sort arr #'<))
     (loop for i from 0 below (1- (min (1+ (- R L)) 4040))
           do (loop for j from (1+ i) below (min (1+ (- R L)) 4040) while (not (zerop ans))
                    do (setf ans (min ans (rem (* (aref arr i) (aref arr j)) 2019)))))
     (princ ans))