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
  list($townNum, $move) = explode(' ', input());
  $to = explode(' ', input());
  $current = 1;
  $visited = $moved = [];

  for($i = 1; $i <= $move; $i++) {
    if (isset($visited[$current])) {
      break;
    }
    $visited[$current] = $i;
    $moved[$i] = $current;
    
    $_tmp = $to[$current - 1];
    $current = $_tmp;
  }

$base = $visited[$current];
$loop = $i - $base;
$_moved = ($move + 1 - $base) % $loop;

echo $moved[$base + $_moved];

function input()
{
  return trim(fgets(STDIN));
}