403. Josephus Problem Using Circular Linked List

There are n people standing in a circle, numbered 1 to n. Starting from person 1, every k-th person is eliminated, continuing around the circle until one remains. Return the position (1-indexed) of the last survivor. Input: 'n, k'.

Input: 'n, k'.

Output: Integer — survivor position (1-indexed).

Examples

Input: 7, 3
Output: 4
Explanation: Survivor is position 4.

Input: 5, 2
Output: 3
Explanation: Survivor is position 3.

Input: 1, 1
Output: 1
Explanation: Only one person.

Constraints

• 1<=n<=10^5
• 1<=k<=10^5

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