Problem:
Score: 400 points

Problem Statement

The Kingdom of Takahashi has N towns, numbered 1 through N.

There is one teleporter in each town. The teleporter in Town i (1 \leq i \leq N) sends you to Town A_i.

Takahashi, the king, loves the positive integer K. The selfish king wonders what town he will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Help the king by writing a program that answers this question.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

1 \leq K \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \dots A_N

Output

Print the integer representing the town the king will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Sample Input 1

4 5
3 2 4 1

Sample Output 1

4

If we start at Town 1 and use the teleporter 5 times, our travel will be as follows: 1 \to 3 \to 4 \to 1 \to 3 \to 4.

Sample Input 2

6 727202214173249351
6 5 2 5 3 2

Sample Output 2

2

Solution in PHP (7.4.4) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d %d", $N, $K);
$A = array_map('intval', explode(' ', trim(fgets(STDIN))));
$cursor = 1;
$line = ['1'];
$visited = ['1' => 1];
$next = null;
$ans = null;
while(true) {
    $next = $A[$cursor - 1];
    if (isset($visited[$next])) {
        $pos = array_search($next, $line);
        $K -= $pos;
        $loop = count($line) - $pos;
        $ans = $line[$pos + $K % $loop];
        break;
    } else {
        $line[] = $next;
		$visited[$next] = 1;
    }
    if (count($line) === $K + 1) {
        $ans = $next;
        break;
    }
    $cursor = $next;
}
printf("%d", $ans);