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: Wrong Answer)

use std::io;

fn main() {
    let nums = read_ints();
    let (n, k) = (nums[0], nums[1]);
    let a: Vec<_> = read_ints().into_iter().map(|x| x-1).collect();

    let mut order: Vec<Option<usize>> = vec![None; n];
    order[0] = Some(0);
    let mut hist = vec![0];
    
    let mut before_loop: &[usize] = &[];
    let mut closed_loop: &[usize] = &[];

    for i in 1.. {
        let next = a[*hist.last().unwrap()];
        if let Some(c) = order[next] {
            // loop detected
            before_loop = &hist[..c];
            closed_loop = &hist[c..];
            break;
        }
        order[next] = Some(i);
        hist.push(next);
    }

    let ans = if (k - 1) < before_loop.len() {
        before_loop[k-1]
    } else {
        let last = (k - before_loop.len()) % closed_loop.len();
        closed_loop[last]
    } + 1;
    println!("{}", ans);
}

fn read_line() -> String {
    let mut line = String::new();
    io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

fn read_ints() -> Vec<usize> {
    read_line()
        .split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect()
}