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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

require 'pp'
$DEBUG ? define_method(:dpp){|e|pp e} : define_method(:dpp){|e|}

# 空白区切の入力値を数値の配列で返却する
def gets_i_list()
  gets.chomp.split(" ").map(&:to_i)
end
N, K = gets_i_list
a_list = [0]
a_list += gets_i_list

to = a_list[1]
route = [1]
count = 0
K.times do |i|
  if route.include?(to)
    remain_count = (K - route.size)
    rloop = route.slice(route.index(to), route.size)
    puts rloop[remain_count % rloop.size]
    exit
  end
  route.push(to)
  to = a_list[to]
end
puts route.last