The Last Person Standing

In this problem, you are given two integers n and k, where n represents the number of people arranged in a circle and k is the count for consecutive eliminations. Starting from the first person, every k^th person is eliminated from the circle until only one person remains. The task is to determine the position (1-indexed) of the last person remaining.

The recurrence relation for this problem, often known as the Josephus problem, is given by:

$$J(n, k) = \begin{cases} 1 & \text{if } n = 1,\\ ((J(n-1, k) + k - 1) \mod n) + 1 & \text{if } n > 1. \end{cases}$$

Implement the function to compute this value efficiently.

inputFormat

The input consists of two space-separated integers:

• n: the number of persons in the circle.
• k: the step rate determining which person is eliminated in each round.

outputFormat

Output a single integer representing the position (1-indexed) of the last person remaining.

## sample

5 2

3