# Generate Array whose sum of all K-size subarrays divided by N leaves remainder X

Given three integer N, K and X, the task is to create an array of length N suach that sum of all its K-length subarrays modulo N is X.

Examples:

Input: N = 6, K = 3, X = 3
Output: 9 6 6 9 6 6
Explanation:
All subarrays of length 3 and their respective sum%N values are as follows:
[9, 6, 6] Sum = 21 % 6 = 3
[6, 6, 9] sum = 21 % 6 = 3
[6, 9, 6] sum = 21 % 6 = 3
[9, 6, 6] sum = 21 % 6 = 3
Since all its subarrays have sum % N = X (=3), the generated array is valid.

Input: N = 4, K = 2, X = 2
Output: 6 4 6 4

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

Approach:
We can observe that in order to make the sum of any subarray of size K modulo N to be equal to X, the subarray needs to have a K – 1 elements equal to N and 1 element equal to N + X.

Illustration:

If N = 6, K = 3, X = 3
Here a K length subarray needs to be a permutation of {9, 6, 6} where 2 (K – 1) elements are divisible by 6 and 1 element has modulo N equal to X( 9%6 = 3)
Sum of subarray % N = (21 % 6) = 3 (same as X)
Hence, each K length

Hence, follow the steps below to solve the problem:

• Iterate i from 0 to N – 1, to print the ith element of the required subarray.
• If i % K is equal to 0, print N + X. Otherwise, for all other values of i, print N.
• This ensures that every possible K-length subarray has a sum K*N + X. Hence sum modulo N is X for all such subarrays.

Below is the implementation of the above approach.

## C++

 `// C++ implementation of the ` `// above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Funtion prints the required array ` `void` `createArray(``int` `n, ``int` `k, ``int` `x) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``// First element of each K ` `        ``// length subarrays ` `        ``if` `(i % k == 0) { ` `            ``cout << x + n << ``" "``; ` `        ``} ` `        ``else` `{ ` `            ``cout << n << ``" "``; ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Program ` `int` `main() ` `{ ` ` `  `    ``int` `N = 6, K = 3, X = 3; ` `    ``createArray(N, K, X); ` `} `

## Java

 `// Java implementation of the above approach ` `import` `java.util.*; ` `class` `GFG{ ` ` `  `// Function prints the required array ` `static` `void` `createArray(``int` `n, ``int` `k, ``int` `x) ` `{ ` `    ``for``(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `         `  `       ``// First element of each K ` `       ``// length subarrays ` `       ``if` `(i % k == ``0``)  ` `       ``{ ` `           ``System.out.print((x + n) + ``" "``); ` `       ``} ` `       ``else` `       ``{ ` `           ``System.out.print(n + ``" "``); ` `       ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `N = ``6``, K = ``3``, X = ``3``; ` `     `  `    ``createArray(N, K, X); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech `

## Python3

 `# Python3 implementation of the  ` `# above approach  ` ` `  `# Funtion prints the required array  ` `def` `createArray(n, k, x): ` `     `  `    ``for` `i ``in` `range``(n): ` `         `  `        ``# First element of each K ` `        ``# length subarrays ` `        ``if` `(i ``%` `k ``=``=` `0``): ` `            ``print``(x ``+` `n, end ``=` `" "``) ` `        ``else` `: ` `            ``print``(n, end ``=` `" "``) ` ` `  `# Driver code ` `N ``=` `6` `K ``=` `3` `X ``=` `3` ` `  `createArray(N, K, X) ` ` `  `# This code is contributed by Vishal Maurya. `

## C#

 `// C# implementation of the above approach ` `using` `System; ` `class` `GFG{ ` ` `  `// Function prints the required array ` `static` `void` `createArray(``int` `n, ``int` `k, ``int` `x) ` `{ ` `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{ ` `        `  `       ``// First element of each K ` `       ``// length subarrays ` `       ``if` `(i % k == 0)  ` `       ``{ ` `           ``Console.Write((x + n) + ``" "``); ` `       ``} ` `       ``else` `       ``{ ` `           ``Console.Write(n + ``" "``); ` `       ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `N = 6, K = 3, X = 3; ` `     `  `    ``createArray(N, K, X); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech `

Output:

```9 6 6 9 6 6
```

Time Complexity: O(N)
Auxiliary Space: O(1) My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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Improved By : vishu2908, Code_Mech