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 $s = <>;
my ($N,$K) = split(/ /,$s);

$s = <>;
my @DB = split (/ /,$s);
my %flag;
my $next = 1;
for(my $i=0;$i<$K;$i++){
    #print "now $next\n";
    if( $flag{$next}< 1 ){
        $flag{$next} = $i;
    }else{
        #print "still came  $i -$flag{$next} \n";
        my $mod =  $i -$flag{$next};
        if( ($K-$i) > $mod ){
          #print "$i + int((($K-$i)-($K-$i)%$mod)/$mod)*$mod\n";
          $i = $i + int((($K-$i)-($K-$i)%$mod)/$mod)*$mod-$mod;
        }
    }
    $next = $DB[$next-1];
    #print "i$i\n";
    #print  "nx $next\n";
}
print "$next"