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)

cs = Array.new(N + 1, 0)
i, x, y = 1, [], []
# xは初めて訪れた所を記録している→そうステップ数　= x.size
# yは一回訪れたところを記録する→周期　= y.size

until cs[i] == 2
    (cs[i].zero? ? x : y) << i
    cs[i] += 1
    i = A[i - 1]
end

puts K < x.size ? x[K] : y[(K - x.size) % (y.size)]