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 Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use std::fmt::Debug;
use std::str::FromStr;

#[allow(dead_code)]
#[allow(deprecated)]
fn read_line_from_stdin() -> String {
    let mut buffer = String::new();
    std::io::stdin().read_line(&mut buffer).unwrap();
    buffer.trim_right().to_owned()
}

#[allow(dead_code)]
#[allow(deprecated)]
fn parse_line_to_single<T>() -> T
where
    T: FromStr,
    T::Err: Debug,
{
    let mut buffer = String::new();
    std::io::stdin().read_line(&mut buffer).unwrap();
    T::from_str(buffer.trim_right()).unwrap()
}

#[allow(dead_code)]
#[allow(deprecated)]
fn parse_line_to_multiple<T>() -> Vec<T>
where
    T: FromStr,
    T::Err: Debug,
{
    let mut buffer = String::new();
    std::io::stdin().read_line(&mut buffer).unwrap();
    buffer
        .trim_right()
        .split_whitespace()
        .flat_map(|s| T::from_str(s))
        .collect()
}

macro_rules! parse_line {
    [$( $x:tt : $t:ty ),+] => {
        //declare variables
        $( let $x: $t; )+
        {
            use std::str::FromStr;
            // read
            let mut buf = String::new();
            std::io::stdin().read_line(&mut buf).unwrap();
            #[allow(deprecated)]
            let mut splits = buf.trim_right().split_whitespace();
            // assign each variable
            $(
                $x = splits.next().and_then(|s| <$t>::from_str(s).ok()).unwrap();
            )+
            // all strs should be used for assignment
            assert!(splits.next().is_none());
        }
    };
}

#[derive(Debug, Clone, PartialEq)]
struct Book {
    price: usize,
    skills: Vec<usize>,
}

fn pow(base: usize, mut power: usize) -> usize {
    let mut value = base;
    while power > 1 {
        value *= base;
        power -= 1;
    }

    value
}

fn main() {
    parse_line![_town_count: usize, desired_move_count: usize];

    let transporters = parse_line_to_multiple::<usize>();

    let mut current_town = 1;
    let mut move_histories = vec![];

    loop {
        if move_histories.len() == desired_move_count {
            println!("{}", current_town);
            break;
        }
        if move_histories.contains(&current_town) {
            let remaining_movement = desired_move_count - move_histories.len();

            let first_loop_index = {
                let mut i = 0;
                loop {
                    if move_histories[i] == current_town {
                        break;
                    }
                    i += 1;
                }
                i
            };

            let loop_length = move_histories.len() - first_loop_index;
            let index_diff = remaining_movement % loop_length;
            let final_town = move_histories[first_loop_index + index_diff];
            println!("{}", final_town);
            break;
        }
        move_histories.push(current_town);
        let town_index = current_town - 1;
        current_town = transporters[town_index];
    }
}