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: Wrong Answer)

program test
integer,allocatable::x(:),y(:),z(:)
integer::r,l,ans,k,i,check
check=1
read(*,*)l,r
if(r-l+1>=2019)then
	ans=0
else 
	k=r-l+1
    allocate(x(0:k))
    allocate(y(1:k))
    allocate(z(1:k))
    do i=1,k
    	x(i)=l+i-1
    end do
    do i=1,k
    	z(i)=mod(x(i),673)
    end do
		if(minval(z)==0 .and. k>=3)then
        	ans=0
        else
    		x(0)=x(k)
    		do i=1,k
    		y(i)=mod(x(i-1)*x(i),2019)
    		end do
  			ans=minval(y)
        end if
end if
print*,ans
end program test