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 C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
using ll = int64_t;

int main() {
  ll l, r;
  cin >> l >> r;

  set<int> mods;
  for (ll i = l; i <= r; i++) {
    mods.insert(i % 2019);
  }

  vector<int> m;
  for (auto itr = mods.begin(); itr != mods.end(); itr++) {
    m.push_back(*itr);
  }

  int ans = 2020;
  for (int i = 0; i < m.size(); i++) {
    for (int j = i + 1; j < m.size(); j++) {
      ans = min(ans, (m[i] * m[j]) % 2019);
    }
  }

  cout << ans << endl;
}