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


[$N,$T] = fscanf(STDIN, "%d%d");
$town = fscanf(STDIN, str_repeat("%d", $N));
$tele = array_fill(1,$N,0);
$tele[1] = 1;
$i = 0;
$now = 1;
while($T--){
    $now = $town[$now-1];

    if($tele[$now] === 1){
        $start = $now;
        $now = $town[$now-1];
        $count = 1;
        while($now != $start){
            $now = $town[$now-1];
            $count++;
        }
        $T %= $count;
        while($T--){
            $now = $town[$now-1];

        }
        break;
    }else{
        $tele[$now] = 1;
    }


}

echo $now;