Shifting

题意翻译

有一个函数操作，参数为一个数组和一个k，操作内容是将数组分成k个一组，将每一组内的k个元素全部左移一位，首个元素左移后被挤到最后一个 最后几个如果不足k个也要移动 求对原排列[1,2,3,…,N] 做 n-1 次操作，每次k=2,3,4,…,N 后 最终数组的形态

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&gt;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.

输入输出格式

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

输入样例 #1

2

输出样例 #1

2 1 

输入样例 #2

3

输出样例 #2

1 3 2 

输入样例 #3

4

输出样例 #3

4 2 3 1 

说明

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] $