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)

lines = []
while line = gets
    lines << line.chomp.split(' ').map(&:to_i)
end

n = lines[0][0]
k = lines[0][1]
go_to = lines[1]

current_town = 1
travel_root = []
visited = []
for i in 1..n do
  visited[i-1] = false
end
for i in 1..n+1 do
  travel_root.push(current_town)
  if visited[current_town - 1] then
    first_visit = travel_root.index(current_town)
    second_visit = i - 1
    loop_num = second_visit - first_visit
    break
  end
  visited[current_town - 1] = true
  current_town = go_to[current_town - 1]
end
  
if first_visit == 0 then
  print travel_root[k % loop_num]
elsif k <= first_visit then
  print travel_root[k]
else
  num = (k - first_visit)
  print travel_root[(num % loop_num) + first_visit]
end