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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

      PROGRAM RemainderMinimization2019
      IMPLICIT NONE
      integer(16) :: l,r, i,j
      integer(16) :: ans=2*10**8+1,buffer
      
      read*,l,r
      
      do i = l,r-1
        do j = i+1,r
          buffer = mod(i*j,2019)
          ans = min( ans,buffer )
          if( ans==0 )then
            print*,ans;stop
          end if
        end do
      end do
      
      print*,ans
      
      
      
      
      
      END PROGRAM