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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import math
from collections import deque
import sys
sys.setrecursionlimit(10**9)

def main():
    N,K = map(int,input().split())
    A = list(map(int,input().split()))

    graph = [0] * (N+1)
    for i in range(N+1): #1-indexed
        f = i
        t = A[i-1]
        graph[f] = t


    def solve():
        visited = []
        stack = deque([1])
        x = 1
        count = 0
        while len(stack) > 0:
            x = stack.pop()
            if x in visited:
                break

            visited.append(x)
            stack.append(graph[x])
            count += 1

            if count == K:
                print(stack.pop())
                exit()

        loop_head = x
        head_index = visited.index(loop_head)
        loop_len = len(visited) - head_index

        r = (K-head_index)%loop_len
        print(visited[head_index:][r])


    solve()


if __name__ == "__main__":
  main()