After falling asleep, Max dreamt about a problem:

You are given a permutation, $P$, of $N$ numbers from $1$ to $N$. Initially, set $A=P$. A move operation is when, for every index $i$ in $A$ simultaneously, the element at index $i$ is moved to index $P_i$. Apply the move operation $K$ times.

Since Max was dreaming, he could not solve this problem.

Can you solve Max's dream?

Constraints

$1\le P_i\le N$

Subtask 1 [30%]

$1\le N,K\le {10}^3$

Subtask 2 [70%]

$1\le N\le {10}^5$

$1\le K\le {10}^{18}$

Input Specification

The first line will contain $N$ and $K$, the number of elements in the permutation and the number of times to perform the operation, respectively.

The next line will contain $N$ space-separated integers, $P_i$, the elements of the permutation.

Output Specification

Output the permutation, $A$, after applying the operation $K$ times.

Sample Input 1

5 3
5 3 2 1 4

Sample Output 1

5 2 3 1 4

Explanation for Sample Output 1

After the first operation, the permutation becomes $[1,2,3,4,5]$.

After the second operation, the permutation becomes $[4,3,2,5,1]$.

After the third and final operation, the permutation becomes $[5,2,3,1,4]$.

Sample Input 2

5 1000000000000000000
5 1 2 3 4

Sample Output 2

5 1 2 3 4