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