Josephus Permutation

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Time limit2sMemory limit256 MB

Summary

Simulate the Josephus elimination order for N people counting off every K-th person in a circle and print the removal sequence.

Level: Easy3 of 10
Topics: Queue, Simulation, Implementation
Solved: No attempts yet

Problem

N people numbered from 1 to N sit in a circle. Given a positive integer K, repeatedly remove the K-th remaining person while counting around the circle. After a person is removed, counting resumes from the next remaining person. The order in which all people are removed is called the (N, K)-Josephus permutation.

Given N and K, print the (N, K)-Josephus permutation.

Input

The first line contains N and K separated by a space.

1 <= K <= N <= 5,000

Output

Print the removed numbers in order, enclosed in angle brackets < and >. Separate adjacent numbers with a comma followed by one space: , .

Examples1

Example 1
Input
```
7 3
```
Expected output
```
<3, 6, 2, 7, 5, 1, 4>
```