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)

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

ofs = []
line = [1]
hash = {}
hash[1] = 0
piv = 1

n.times do |c|
  piv = a[piv-1]
  if line.include?(piv)
    ofs = line.take(hash[piv])
    line = line.drop(hash[piv])
    break
  end
  hash[piv] = c+1
  line << piv
end

if k < ofs.length
  puts("#{ofs[k]}")
else
  k -= ofs.length
  puts("#{line[k%line.length]}")
end