# Create an array of size N with sum S such that no subarray exists with sum S or S-K

Given a number N and an integer S, the task is to create an array of N integers such that sum of all elements equals to S and print an element K where 0 ≤ K ≤ S, such that there exists no subarray with sum equals to K or (S – K).
If no such array is possible then print “-1”.

Note: There can be more than one value for K. You can print any one of them.

Examples:

Input: N = 1, S = 4
Output: {4}
K = 2
Explanation:
There exists an array {4} whose sum is 4.
From all possible value of K i.e., 0 ≤ K ≤ 4, K = 1, 2, and 3 satisfy the given conditions.
For K = 2, there is no subarray whose sum is 2 or S – K i.e., 4 – 2 = 2.

Input: N = 3, S = 8
Output: {2, 2, 4}
K = 1
Explanation:
There exists an array {2, 2, 4} and there exists K as 1 such that there is no subarray whose sum is 1 and S – K i.e., 8 – 1 = 7.

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

Approach: To solve the problem mentioned above we have to observe that:

1. If 2 * N > S then there is no array possible.
For Example:

For N = 3 and S = 4, then the possible arrays are {1, 2, 1}, {1, 1, 2}, {2, 1, 1}.
The possible values for K are 0, 1, 2, 3 (0 < = k < = S).
But there is no value for K which satisfy the condition.
So the solution to this is not possible.

2. An array is only possible if 2 * N <= S and the array can be created using elements (N-1) times 2 and the last element as S – (2 * (N – 1)) and K will always be 1.

Below is the implementation of the above approach:

## C++

 `// C++ for the above approach ` `#include ` `using` `namespace` `std; ` `     `  `// Function to create an array with ` `// N elements with sum as S such that ` `// the given conditions satisfy ` `void` `createArray(``int` `n, ``int` `s) ` `{ ` `     `  `    ``// Check if the solution exists ` `    ``if` `(2 * n <= s) ` `    ``{ ` ` `  `        ``// Print the array as ` `        ``// print (n-1) elments ` `        ``// of array as 2 ` `        ``for``(``int` `i = 0; i < n - 1; i++)  ` `        ``{ ` `           ``cout << ``"2"` `<< ``" "``; ` `           ``s -= 2; ` `        ``} ` ` `  `        ``// Print the last element ` `        ``// of the array ` `        ``cout << s << endl; ` ` `  `        ``// Print the value of k ` `        ``cout << ``"1"` `<< endl; ` `    ``} ` `    ``else` `     `  `        ``// If solution doesnot exists ` `        ``cout << ``"-1"` `<< endl; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `     `  `    ``// Given N and sum S ` `    ``int` `N = 1; ` `    ``int` `S = 4; ` ` `  `    ``// Function call ` `    ``createArray(N, S); ` `} ` ` `  `// This code is contributed by Ritik Bansal `

## Java

 `// Java for the above approach ` `class` `GFG{ ` `     `  `// Function to create an array with ` `// N elements with sum as S such that ` `// the given conditions satisfy ` `static` `void` `createArray(``int` `n, ``int` `s) ` `{ ` ` `  `    ``// Check if the solution exists ` `    ``if` `(``2` `* n <= s) ` `    ``{ ` ` `  `        ``// Print the array as ` `        ``// print (n-1) elments ` `        ``// of array as 2 ` `        ``for` `(``int` `i = ``0``; i < n - ``1``; i++)  ` `        ``{ ` `            ``System.out.print(``2` `+ ``" "``); ` `            ``s -= ``2``; ` `        ``} ` ` `  `        ``// Print the last element ` `        ``// of the array ` `        ``System.out.println(s); ` ` `  `        ``// Print the value of k ` `        ``System.out.println(``1``); ` `    ``} ` `    ``else` `     `  `        ``// If solution doesnot exists ` `        ``System.out.print(``"-1"``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args)  ` `{ ` ` `  `    ``// Given N and sum S ` `    ``int` `N = ``1``; ` `    ``int` `S = ``4``; ` ` `  `    ``// Function call ` `    ``createArray(N, S); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 for the above approach ` ` `  `# Function to create an array with ` `# N elements with sum as S such that ` `# the given conditions satisfy ` `def` `createArray(n, s): ` `  `  `    ``# Check if the solution exists ` `    ``if` `(``2` `*` `n<``=` `s):              ` `         `  `        ``# Print the array as ` `        ``# print (n-1) elments  ` `        ``# of array as 2 ` `        ``for` `i ``in` `range``(n``-``1``): ` `            ``print``(``2``, end ``=``" "``) ` `            ``s``-``=` `2` `             `  `        ``# Print the last element ` `        ``# of the array  ` `        ``print``(s)  ` `         `  `        ``# Print the value of k  ` `        ``print``(``1``) ` `    ``else``: ` `        ``# If solution doesnot exists ` `        ``print``(``'-1'``) ` ` `  ` `  `# Driver Code  ` ` `  `# Given N and sum S   ` `N ``=` `1` `S ``=` `4` ` `  `# Function call ` `createArray(N, S) `

## C#

 `// C# program for the above approach ` `using` `System; ` `class` `GFG{ ` `     `  `// Function to create an array with ` `// N elements with sum as S such that ` `// the given conditions satisfy ` `static` `void` `createArray(``int` `n, ``int` `s) ` `{ ` `     `  `    ``// Check if the solution exists ` `    ``if` `(2 * n <= s) ` `    ``{ ` ` `  `        ``// Print the array as ` `        ``// print (n-1) elments ` `        ``// of array as 2 ` `        ``for``(``int` `i = 0; i < n - 1; i++)  ` `        ``{ ` `           ``Console.Write(2 + ``" "``); ` `           ``s -= 2; ` `        ``} ` ` `  `        ``// Print the last element ` `        ``// of the array ` `        ``Console.WriteLine(s); ` ` `  `        ``// Print the value of k ` `        ``Console.WriteLine(1); ` `    ``} ` `    ``else` `     `  `        ``// If solution doesnot exists ` `        ``Console.Write(``"-1"``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main()  ` `{ ` ` `  `    ``// Given N and sum S ` `    ``int` `N = 1; ` `    ``int` `S = 4; ` ` `  `    ``// Function call ` `    ``createArray(N, S); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech `

Output:

```4
1
```

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 : 29AjayKumar, Code_Mech, btc_148