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)

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

fn main() {
    let (n, k) = {
        let nm = get_line().split_whitespace()
            .map(|e| e.parse().unwrap())
            .collect::<Vec<usize>>();
        (nm[0], nm[1])
    };

    let mut k = k;

    let dist: Vec<usize> = get_line().split_whitespace()
        .map(|e| e.parse::<usize>().unwrap() - 1)
        .collect();

    let mut seen: Vec<bool> = vec![false; n];
    let mut current = 0;

    let mut count = 0;

    loop {
        seen[current] = true;
        count += 1;
        current = dist[current];

        if seen[current] { break; }
    }
    // ここでどこかに返ってきた
    // 1から今いる地点まで何回か => count
    // 残り
    if k <= count {
        let mut count = 0;
        loop {
            count += 1;
            current = dist[current];
            if count == k { break; }
        }
        println!("{}", current + 1);
    }
    k -= count;
    // 今いる地点から今いる地点に戻ってくるまで何回か
    count = 0;
    seen = vec![false; n];
    loop {
        seen[current] = true;
        count += 1;
        current = dist[current];

        if seen[current] { break; }
    }


    let diff = k % count;
    for _ in 0..diff {
        current = dist[current];
    }

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