# Find K such that |A – K| = |B – K|

• Last Updated : 07 Mar, 2022

Given two integers A and B where (A ≠ B). The task is to find K such that |A – K| = |B – K|. If no such K exists then print -1.

Examples:

Input: A = 2, B = 16
Output:
|2 – 9| = |16 – 9| = 7

Input: A = 5, B = 2
Output: -1

Approach: It is given that A ≠ B. So let A < B then there are three cases:

• K < A: This gives A – K = B – K which gives A = B which is false.
• K > B: This gives K – A = K – B which is also false.
• A ≤ K ≤ B: This gives K – A = B – K which gives 2 * K = A + B

If A + B is odd, there is thus no solution. If A + B is even then the answer is (A + B) / 2.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to find k such that` `// |a - k| = |b - k|` `int` `find_k(``int` `a, ``int` `b)` `{` `    ``// If (a + b) is even` `    ``if` `((a + b) % 2 == 0)` `        ``return` `((a + b) / 2);`   `    ``return` `-1;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `a = 2, b = 16;`   `    ``cout << find_k(a, b);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `class` `GFG` `{` `    `  `// Function to find k such that` `// |a - k| = |b - k|` `static` `int` `find_k(``int` `a, ``int` `b)` `{` `    ``// If (a + b) is even` `    ``if` `((a + b) % ``2` `== ``0``)` `        ``return` `((a + b) / ``2``);`   `    ``return` `-``1``;` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `a = ``2``, b = ``16``;`   `    ``System.out.println(find_k(a, b));` `}` `}`   `// This code is contributed by Code_Mech`

## Python3

 `# Python3 implementation of the approach `   `# Function to find k such that ` `# |a - k| = |b - k| ` `def` `find_k(a, b) :`   `    ``# If (a + b) is even ` `    ``if` `((a ``+` `b) ``%` `2` `=``=` `0``) : ` `        ``return` `((a ``+` `b) ``/``/` `2``); `   `    ``return` `-``1``; `   `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `: `   `    ``a ``=` `2``; b ``=` `16``; `   `    ``print``(find_k(a, b)); `   `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach ` `using` `System;`   `class` `GFG` `{` `    `  `// Function to find k such that` `// |a - k| = |b - k|` `static` `int` `find_k(``int` `a, ``int` `b)` `{` `    ``// If (a + b) is even` `    ``if` `((a + b) % 2 == 0)` `        ``return` `((a + b) / 2);`   `    ``return` `-1;` `}`   `// Driver code` `public` `static` `void` `Main()` `{` `    ``int` `a = 2, b = 16;`   `    ``Console.Write(find_k(a, b));` `}` `}`   `// This code is contributed by chitranayal`

## Javascript

 ``

Output

`9`

Time Complexity: O(1)

Auxiliary Space: O(1)

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