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 Python (3.8.2) (judge verdict: Runtime Error)

import numpy as np 
import sys 

readline = sys.stdin.readline

N, K = map(int, readline().split())
A = list(map(int, readline().split()))

# 愚直にやると計算量O(K)でTLEになる
# 同じ街にいったら操作打ち切りで配列を完結させる

# Teleport順の配列を作る
teleport = {1: True}
next_town = 1
for i in range(K):
    next_town = A[next_town - 1] # next_townがintで与えられる
    try: # 辞書を使用してO[1]で判定する
        teleport[next_town]
        dupulicate_town = next_town
        # 辞書をリストに変換
        teleport = list(teleport.keys())
        dupulicate_index = teleport.index(dupulicate_town)
        dupulicate_list = teleport[dupulicate_index:]
        break
    except KeyError:
        teleport[next_town] = True


if len(teleport) - 1 == K:
    print(teleport[-1])
else: # ループに入る場合
    consumption = len(teleport) - 1
    roop_num = K - consumption
    roop_index = roop_num % len(dupulicate_list)
    if roop_index == 0:
        print(dupulicate_list[-1])
    else:
        print(dupulicate_list[roop_index - 1])