Bloomberg面经准备: Josephus problem

Given a circular single linked list.Write a program that deletes every kth node until only one node is left. 
After kth node is deleted, start the procedure from (k+1)th node. 
e.g.list is 1->2->3->4->5->1 
k=3 
1. You are at 1, delete 3. 
List is: 1->2->4->5->1 
2. You are at 4, delete 1 
List is: 2->4->5->2 
3. You are at 2,delete 5 
List is: 2->4->2 
4. You are at 2, delete 2 
List is: 4 
Return 4. 

How efficient you can do it?