10721: ABC133 - C - Remainder Minimization 2019
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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:
```
$L$ $R$
```
```
$L$ $R$
```
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.
- $0 \leq L < R \leq 2 \times 10^9$
- $0 \leq L < R \leq 2 \times 10^9$
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: $(i, j) = (4, 5)$.