Problem Description

Define one operation on a sequence $a$ as setting $b_i \gets a_{a_i}$, and then setting $a_i \gets b_i$, where $i \in [1,n]$.

You are given a sequence $a$ of length $n$. Ask for the sequence after performing the operation on $a$ exactly $k$ times.

Input Format

The first line contains two integers $n, k$.

The second line contains $n$ integers representing the sequence $a$.

Output Format

Output one line with $n$ integers, representing the sequence $a$ after $k$ operations.

5 2
2 5 4 3 1

2 5 3 4 1

20 233
1 1 5 6 8 15 10 11 18 14 4 16 16 11 3 5 1 15 4 5

1 1 4 5 6 8 4 15 5 6 3 11 11 15 11 4 1 8 3 4

Hint

Sample Explanation

For Sample $1$, the changes of $a$ are as follows:

Constraints

This problem uses bundled testdata.

Property $\text A$: $0 \le k \le 10^3$.
Property $\text B$: $a_i = i \bmod n + 1$.
Property $\text C$: $a$ is a permutation of $[1,n]$.

For $100\%$ of the testdata, $1 \le n \le 5 \times 10^5$, $0 \le k \le 10^9$, $1 \le a_i \le n$.

Translated by ChatGPT 5