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: Accepted)

nums=gets.strip.split(" ").map do |i|
  i.to_i
end
n=nums[0]
k=nums[1]
s=nums=gets.strip.split(" ").map do |i|
  i.to_i
end
now=1
tele_num=0
a = Array.new(n,nil)
a[0] = 0
flag=false
#puts "tele_num #{tele_num} now #{now}"
while tele_num < k
  next_pos = s[now-1]
  tele_num+=1
  #puts "tele_num #{tele_num} next_pos #{next_pos}"
  if a[next_pos].nil? || flag
    a[next_pos] = tele_num
  else
    #puts "tele_numff #{tele_num}"
    #puts "next_pos #{a[next_pos]}"
    loop_num = tele_num - a[next_pos]
    #puts "loop_num #{loop_num}"
    t=((k - tele_num) / loop_num).to_i 

    tele_num += (t*loop_num)
    flag=true
  end
  now = next_pos
end
puts now