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 Perl (5.26.1) (judge verdict: Accepted)

my ($n,$k) = split(/\s+/, <>);
my (@a) = (0, split(/\s+/, <>));
my @visited = ();

my $c = 1;
my $pos = 1;
while (!$visited[$pos]) {
    $visited[$pos] = $c;
    $pos = $a[$pos];
    $c++;
}

$c -= $visited[$pos];

my $current = 1;
while ($k-->0) {
    $current = $a[$current];
    if ($current == $pos) {
	$k %= $c;
    }
}

print "$current\n";