Last Remaining Person: A Josephus Problem Variation

You are given n people numbered from 1 to n arranged in a circle and a positive integer k. Starting from the first person, every k-th person is eliminated from the circle. The process is repeated with the remaining people until only one person remains.

The elimination index is updated using the formula:

$$ index = (index + k - 1) \mod \text{current_size} $$

Your task is to determine the 1-based position of the last remaining person.

inputFormat

The input consists of a single line containing two integers n and k separated by space.

Constraints:

• 1 ≤ n ≤ 10⁵ (depending on the problem setting)
• 1 ≤ k ≤ 10⁵

outputFormat

Output the 1-based index of the last remaining person.

5 2

3