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 ($1 \le k \le n$) 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 ,($b_k$)
• determines the sequence of numbers ($a_k$),
• writes that sequence to the standard output.

Input

In the first line of the standard input there are two positive integers $n$ and $l$ ($1 \le n, l \le 1\,000\,000$). In the consecutive $n$ lines there are successive elements of the sequence ($b_k$), one per line. In the $(k+1)$-st line there is a positive integer $b_k$: the final position of the card from the $k$-th position, $1 \le b_k \le n$.

Output

Your program should write to the standard output $n$ integers: successive elements of the sequence ($a_k$), one per line. In the $k$-th line there should be one number $a_k$: 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 ($a_k$). If there are many such sequences your program should write one of them (arbitrary).

Example

Input

5 2
1
2
5
3
4

Output

1
2
4
5
3

Input 2

5 2
1
2
5
3
4

Output 2

2
1
4
5
3