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: Wrong Answer)

<?php

fscanf(STDIN, "%d%d", $N, $K);

$list = explode(" ", trim(fgets(STDIN)));
$chkarray = array_fill(1, $N, 0);
$count = 0;
$now = 1;
while(true){
    $count++;
    if($chkarray[$now] != 0){
        $before = $chkarray[$now] - 1;
        $loop = $count - $before -1;
        $loop_target = $now;
        break;
    }else{
        $chkarray[$now] = $count;
        $now = $list[$now-1];
        $memo[$count] = $now;
    }
}
$value = $K - $before;
$value = $value - $loop * intdiv($value-1, $loop);
//
//while($value--){
//    $loop_target = $list[$loop_target-1];
//}
echo $memo[$value + $before];