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: Runtime Error)

n,k = gets.split(' ').map(&:to_i)
terepos = gets.split(' ').map(&:to_i)
next_list = [1]
while next_list.length <= [k,200000].min
  # result = next_list.index(terepos[next_list[-1] - 1])
  # if result
  #   roop_index = result
  #   break
  # else
    next_list << terepos[next_list[-1] - 1]
  # end
end
roop_length = next_list.uniq.size
roop_start = next_list.index(next_list[roop_length])
# puts("-------------")
# puts(roop_start)
# puts(roop_length)
# puts("-------------")

if k == next_list.size
  puts(next_list[-1])
else
  puts(next_list[((k + 1 - roop_start) % (roop_length - roop_start) + (roop_length - roop_start) - 1) % (roop_length - roop_start) + roop_start])
end