Problem Statement

A group of people are standing in a circle, numbered from 1 to n. Starting from a specific person, every kth person in the circle is eliminated until only one person remains. The task is to determine the position of the last remaining person.

This is a classic problem in combinatorial mathematics, often referred to as the Josephus Problem.

Examples

Example 1:

Input: n = 7, k = 3
Output: 4

Explanation: The people are numbered from 1 to 7. Starting from 1 and counting every 3rd person, the elimination order is:
1. Eliminate person 3
2. Eliminate person 6
3. Eliminate person 2
4. Eliminate person 7
5. Eliminate person 5
6. Eliminate person 1.
The last person remaining is 4.

Example 2:

Input: n = 5, k = 2
Output: 3

Explanation:
With 5 people and counting every 2nd person, the elimination order is:
1. Eliminate person 2
2. Eliminate person 4
3. Eliminate person 1
4. Eliminate person 5

The last person remaining is 3.