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)

n, k = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)

hash = { 1 => 0}
keiro = [1]
current = 1
nex = nil
count = 0
while true do
  nex = a[current-1]
  keiro.push(nex)
  break unless hash[nex].nil?
  count += 1
  hash[nex] = count
  current = nex
end

if keiro.size - 1 >= k
  puts keiro[k]
  exit
end

start = hash[nex]
loop = keiro[start..-1]

before_loop = keiro.size - loop.size
k = k - before_loop
k = k % (loop.size - 1)
puts loop[k]