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X Olympiad in Informatics 2002/2003
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Problem: Shuffle
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Author: Pawel Parys
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Byteasar has a pack of n cards that he likes to shuffle. The
positions of cards are numbered from 1 to n. Byteasar has
acquired such a skill in shuffling that each time he obtains the same
arrangement, i.e. a card from the k-th position
(1 <= k <= n) always goes to
the same ak-th position. We denote by
bk the position of the k-th card
(i.e. the card initially placed at the k-th position) after
Byteasar repeated shuffling l times.
Task
Write a program which:
- reads from the standard input the numbers n and l
and the sequence of numbers (bk),
- determines the sequence of numbers (ak),
- writes that sequence to the standard output.
Input
In the first line of the standard input there are two positive
integers n and l
(1 <= n, l <= 1000000).
In the consecutive n lines there are successive elements of
the sequence (bk), one per line. In the
(k + 1)-st line there is a positive integer
bk: the final position of the card from the
k-th position, 1 <= bk <= n.
Output
Your program should write to the standard output n integers:
successive elements of the sequence (ak), one
per line. In the k-th line there should be one number
ak: the position of the card from the
k-th position after a single shuffle. You may assume that for
the test data there always exist the desired sequence
(ak). If there are many such sequences your
program should write one of them (arbitrary).
Example
For the following input data:
5 2
1
2
5
3
4
a correct answer is in the following output:
1
2
4
5
3
or:
2
1
4
5
3