# Generate a unique Array of length N with sum of all subarrays divisible by N

Given an integer N, the task is to make an array of unique elements of length N such that all subarrays sum modulo N equals to zero.

Examples:

Input: N = 6
Output: 6 12 18 24 30 36
Explanation:
Since all elements are a muliple of 6. Hence all subarrays add up to a sum divisible by 6.

Input: N = 4
Output: 4 8 12 16

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

Approach:
We can observe that for all subarrays to be divisible by N, the elements of the array need to be a multiple of N.

Illustration:

For N = 4, if we consider the array elements to {4, 8, 12, 16}, All possible subarrays are:
{4}, {8}, {12}, {16}, {4, 8}, {8, 12}, {12, 16}, {4, 8, 12}, {8, 12, 16}, {4, 8, 12, 16}
Hence, all subarrays have a sum divisible by N.

Hence, to solve the problem, we just need to print {N, 2*N, 3*N, ….., N*N} to get the desired array.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the ` `// above approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Funtion to print the required ` `// array ` `void` `makeArray(``int` `a[], ``int` `n) ` `{ ` `    ``// Print the array ` `    ``for` `(``int` `i = 1; i <= n; i++) ` `        ``cout << i * n << ``" "``; ` `} ` ` `  `// Driver Program ` `int` `main() ` `{ ` `    ``int` `N = 6; ` `    ``int` `arr[N]; ` `    ``makeArray(arr, N); ` `} `

## Java

 `// Java program for the above approach ` `class` `GFG{  ` ` `  `// Funtion to print the required ` `// array ` `static` `void` `makeArray(``int` `a[], ``int` `n) ` `{ ` `     `  `    ``// Print the array ` `    ``for``(``int` `i = ``1``; i <= n; i++) ` `       ``System.out.print(i * n + ``" "``); ` `} ` ` `  `// Driver code  ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``int` `N = ``6``; ` `    ``int` `arr[] = ``new` `int``[N]; ` `     `  `    ``makeArray(arr, N); ` `}  ` `}  ` ` `  `// This code is contributed by Pratima Pandey `

## Python3

 `# Python3 implementation of the ` `# above approach ` ` `  `# Function to print the  ` `# required array ` `def` `makeArray(n): ` `     `  `    ``# Print Array  ` `    ``for` `i ``in` `range``(n): ` `        ``print``((i ``+` `1``) ``*` `n, end ``=``" "``) ` ` `  ` `  `# Driver code ` `n ``=` `6``; ` `makeArray(n); `

## C#

 `// C# program for the above approach ` `using` `System; ` `class` `GFG{  ` ` `  `// Funtion to print the required ` `// array ` `static` `void` `makeArray(``int` `[]a, ``int` `n) ` `{ ` `     `  `    ``// Print the array ` `    ``for``(``int` `i = 1; i <= n; i++) ` `    ``Console.Write(i * n + ``" "``); ` `} ` ` `  `// Driver code  ` `public` `static` `void` `Main()  ` `{  ` `    ``int` `N = 6; ` `    ``int` `[]arr = ``new` `int``[N]; ` `     `  `    ``makeArray(arr, N); ` `}  ` `}  ` ` `  `// This code is contributed by Code_Mech `

Output:

```6 12 18 24 30 36
```

Time Complexity: O(N)
Auxiliary Space: O(1)

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Improved By : dewantipandeydp, Code_Mech