Problem10721--ABC133 - C - Remainder Minimization 2019

10721: ABC133 - C - Remainder Minimization 2019

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

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 $(i \times j) \text{ mod } 2019$.

Input

Input is given from Standard Input in the following format:

```
$L$ $R$
```

Output

Print the minimum possible value of $(i \times j) \text{ mod } 2019$ when $i$ and $j$ are chosen under the given condition.

Constraints

-   All values in input are integers.
-   $0 \leq L < R \leq 2 \times 10^9$

Sample 1 Input

2020 2040

Sample 1 Output

2
When $(i, j) = (2020, 2021)$, $(i \times j) \text{ mod } 2019 = 2$.

Sample 2 Input

4 5

Sample 2 Output

20
We have only one choice: $(i, j) = (4, 5)$.

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