CF286B.Shifting

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

John Doe has found the beautiful permutation formula.

Let's take permutation $p=p_{1},p_{2},...,p_{n}$ . Let's define transformation $f$ of this permutation:

where $k$ (k>1) is an integer, the transformation parameter, $r$ is such maximum integer that $rk<=n$ . If $rk=n$ , then elements $p_{rk+1},p_{rk+2}$ and so on are omitted. In other words, the described transformation of permutation $p$ cyclically shifts to the left each consecutive block of length $k$ and the last block with the length equal to the remainder after dividing $n$ by $k$ .

John Doe thinks that permutation $f(f( ... f(p=[1,2,...,n],2) ... ,n-1),n)$ is beautiful. Unfortunately, he cannot quickly find the beautiful permutation he's interested in. That's why he asked you to help him.

Your task is to find a beautiful permutation for the given $n$ . For clarifications, see the notes to the third sample.

输入格式

A single line contains integer $n$ ( $2<=n<=10^{6}$ ).

输出格式

Print $n$ distinct space-separated integers from $1$ to $n$ — a beautiful permutation of size $n$ .

输入输出样例

输入#1
```
2
```
输出#1
```
2 1 
```
输入#2
```
3
```
输出#2
```
1 3 2 
```
输入#3
```
4
```
输出#3
```
4 2 3 1 
```

说明/提示

A note to the third test sample:

$f([1,2,3,4],2)=[2,1,4,3]$
$f([2,1,4,3],3)=[1,4,2,3]$
$f([1,4,2,3],4)=[4,2,3,1]$

首页