# Minimum possible value of (i * j) % 2019

Given two integers L and R, the task is to find the minimum possible value of (i * j) % 2019 where L ≤ i < j ≤ R

Examples:

Input: L = 2020, R = 2040
Output: 2
(2020*2021)%2019 = 2

Input: L = 3, R = 4
Output: 12

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• If R – L ≥ 2019 then answer is 0 as we will get a number in the range which is divisible by 2019 which gives remainder 0.
• If R – L < 2019 then we can run nested loops and find the minimum value.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `const` `int` `MOD = 2019; ` ` `  `// Function to return the minimum ` `// possible value of (i * j) % 2019 ` `int` `min_modulo(``int` `l, ``int` `r) ` `{ ` `    ``// If we can get a number ` `    ``// divisible by 2019 ` `    ``if` `(r - l >= MOD) ` `        ``return` `0; ` `    ``else` `{ ` ` `  `        ``// Find the minimum value ` `        ``// by running nested loops ` `        ``int` `ans = MOD - 1; ` `        ``for` `(``int` `i = l; i <= r; i++) { ` `            ``for` `(``int` `j = i + 1; j <= r; j++) { ` `                ``ans = min(ans, (i * j) % MOD); ` `            ``} ` `        ``} ` `        ``return` `ans; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `l = 2020, r = 2040; ` ` `  `    ``cout << min_modulo(l, r); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` `static` `int` `MOD = ``2019``; ` ` `  `// Function to return the minimum ` `// possible value of (i * j) % 2019 ` `static` `int` `min_modulo(``int` `l, ``int` `r) ` `{ ` `    ``// If we can get a number ` `    ``// divisible by 2019 ` `    ``if` `(r - l >= MOD) ` `        ``return` `0``; ` `    ``else`  `    ``{ ` ` `  `        ``// Find the minimum value ` `        ``// by running nested loops ` `        ``int` `ans = MOD - ``1``; ` `        ``for` `(``int` `i = l; i <= r; i++)  ` `        ``{ ` `            ``for` `(``int` `j = i + ``1``; j <= r; j++) ` `            ``{ ` `                ``ans = Math.min(ans, (i * j) % MOD); ` `            ``} ` `        ``} ` `        ``return` `ans; ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String []args)  ` `{ ` `    ``int` `l = ``2020``, r = ``2040``; ` ` `  `    ``System.out.println(min_modulo(l, r)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python3

 `# Python3 implementation of the approach  ` `MOD ``=` `2019``;  ` ` `  `# Function to return the minimum  ` `# possible value of (i * j) % 2019  ` `def` `min_modulo(l, r) : ` ` `  `    ``# If we can get a number  ` `    ``# divisible by 2019  ` `    ``if` `(r ``-` `l >``=` `MOD) : ` `        ``return` `0``;  ` `    ``else` `: ` ` `  `        ``# Find the minimum value  ` `        ``# by running nested loops  ` `        ``ans ``=` `MOD ``-` `1``;  ` `        ``for` `i ``in` `range``(l, r ``+` `1``) : ` `            ``for` `j ``in` `range``(i ``+` `1``, r ``+` `1``) : ` `                ``ans ``=` `min``(ans, (i ``*` `j) ``%` `MOD);  ` `         `  `        ``return` `ans;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` `     `  `    ``l ``=` `2020``; r ``=` `2040``; ` `     `  `    ``print``(min_modulo(l, r));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `static` `int` `MOD = 2019; ` ` `  `// Function to return the minimum ` `// possible value of (i * j) % 2019 ` `static` `int` `min_modulo(``int` `l, ``int` `r) ` `{ ` `    ``// If we can get a number ` `    ``// divisible by 2019 ` `    ``if` `(r - l >= MOD) ` `        ``return` `0; ` `    ``else` `    ``{ ` ` `  `        ``// Find the minimum value ` `        ``// by running nested loops ` `        ``int` `ans = MOD - 1; ` `        ``for` `(``int` `i = l; i <= r; i++)  ` `        ``{ ` `            ``for` `(``int` `j = i + 1; j <= r; j++) ` `            ``{ ` `                ``ans = Math.Min(ans, (i * j) % MOD); ` `            ``} ` `        ``} ` `        ``return` `ans; ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String []args)  ` `{ ` `    ``int` `l = 2020, r = 2040; ` ` `  `    ``Console.WriteLine(min_modulo(l, r)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```2
```

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Improved By : AnkitRai01, Rajput-Ji