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C - Remainder Minimization 2019

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

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

2020 2040

2

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

4 5

20

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