Shuffle

Memory limit: 32 MB

Byteasar has a pack of cards that he likes to shuffle. The positions of cards are numbered from to . Byteasar has acquired such a skill in shuffling that each time he obtains the same arrangement, i.e. a card from the -th position () always goes to the same -th position. We denote by the position of the -th card (i.e. the card initially placed at the -th position) after Byteasar repeated shuffling times.

Task

Write a program which:

• reads from the standard input the numbers and and the sequence of numbers ,
• determines the sequence of numbers ,
• writes that sequence to the standard output.

Input

In the first line of the standard input there are two positive integers and (, ). In the consecutive lines there are successive elements of the sequence , one per line. In the ()-st line there is a positive integer : the final position of the card from the -th position, .

Output

Your program should write to the standard output integers: successive elements of the sequence , one per line. In the -th line there should be one number : the position of the card from the -th position after a single shuffle. You may assume that for the test data there always exist the desired sequence . If there are many such sequences your program should write one of them (arbitrary).

Example

For the input data:

5 2
1
2
5
3
4

the correct result is:

1
2
4
5
3

or:

2
1
4
5
3

Task author: Pawel Parys.