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
//$N = (int)trim(fgets(STDIN));
//$S = trim(fgets(STDIN));
list($N,$K) = array_map('intval',explode(" ",trim(fgets(STDIN))));
//$s = trim(fgets(STDIN));
$A = array_map('intval',explode(" ",trim(fgets(STDIN))));
foreach($A as $k=>$v) {
  $to[0][$k]=$v-1;
}
$D=60;

for($i=0;$i<$D-1;$i++) {
  for($j=0;$j<$N;$j++) {
    $to[$i+1][$j] = $to[$i][$to[$i][$j]];
  }
}
$v=0;
for($i=$D-1;$i>=0;--$i) {
  $l = 1<<$i;
  if ($l <= $K) {
    $v = $to[$i][$v];
    $K -= $l;
  }
}
printf("%d\n",$v+1);