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: Accepted)

#![allow(non_snake_case)]
use proconio::input;

struct Loop {
    start: usize,
    start_ord: usize,
    period: i64,
}

// ループと最後にいた町のindを返す
fn calc_period(N: usize, K: i64, As: &[i64]) -> (Option<Loop>, usize) {
    let mut loop_start: Option<usize> = None;
    let mut period: Option<i64> = None;

    // テレポートがループする場合があるので、何番目に訪れたかを記録しておく
    // i番目のタウンは何回目の移動で訪れたか
    let mut ord: Vec<Option<usize>> = vec![None; N];
    ord[0] = Some(0);

    // ループを検知する
    let mut town: usize = 0;
    for k in 1..K + 1 {
        let next = As[town] as usize;

        if ord[next].is_some() {
            loop_start = Some(next);
            period = Some((ord[town].unwrap() - ord[next].unwrap() + 1) as i64);
            break;
        } else {
            ord[next] = Some(k as usize);
            town = next;
        }
    }

    // ループ無く終わった場合
    if period == None {
        return (None, town);
    }

    let loop_instance = Loop {
        start: loop_start.unwrap(),
        start_ord: ord[loop_start.unwrap()].unwrap(),
        period: period.unwrap(),
    };

    return (Some(loop_instance), town);
}

fn main() {
    input! {
        N: usize,
        K: i64,
        tmpAs: [i64; N],
    }

    // 問題文では町の番号は1~Nだが、コード中では0~N-1で管理
    let As: Vec<i64> = tmpAs.iter().map(|a| a - 1).collect();

    let tuple = calc_period(N, K, &As);

    if tuple.0.is_none() {
        println!("{}", tuple.1 + 1);
        return;
    }

    let loop_instance = tuple.0.unwrap();

    // periodを知っているので、
    // loop_startまで、できるだけperiod回す、残り
    let start_ord = loop_instance.start_ord;
    let period = loop_instance.period;

    let rest: i64 = (K - start_ord as i64) % period;
    let mut town: usize = loop_instance.start;
    for _k in 0..rest {
        town = As[town] as usize;
    }

    println!("{}", town + 1);
}