Shifting
题目描述
John Doe has found the beautiful permutation formula.
Let's take permutation p=p1,p2,...,pn. 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 prk+1,prk+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.
A single line contains integer n (2≤n≤106).
Print n distinct space-separated integers from 1 to n − a beautiful permutation of size n.
2
2 1
3
1 3 2
4
4 2 3 1
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]
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