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);
  $a = explode(" ", trim(fgets(STDIN)));
  $tosi[0] = 0;
  $tele[0] = 1;
  $i = 1;
  while(1){
    if(isset($tosi[$a[$tele[$i-1]-1]])){
      $s = $tosi[$a[$tele[$i-1]-1]];
      break;
    }
    $tele[$i] = $a[$tele[$i-1]-1];
    $tosi[$a[$tele[$i-1]-1]] = $i;
    $i++;
  }
 // print_r($tele);
  //print_r($tosi);

  $syu = count($tosi)-$s;
  if($k<count($tele)){
    echo $tele[$k-1];
  }else{
    $l = count($tele)-1-$s;
    $t = ($k-$l)%$syu;
    //echo $t;
  echo $tele[$t+$l];
  }