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)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    use std::collections::HashMap;
    let n: u64 = read();
    let mut k: u64 = read();
    let a: Vec<usize> = (0..n).map(|_| read()).map(|x: usize| x - 1).collect();
    let mut set = HashMap::new();
    set.insert(0, 0);
    let mut p: usize = 0;
    let mut count: u64 = 0;
    let dist: u64;
    let start: usize;
    loop {
        count += 1;
        if count == k {
            println!("{}", a[p]+1);
            return;
        }
        let i = set.get(&(a[p]));
        if i.is_some() {
            dist = count - i.unwrap();
            start = a[p];
            break;
        } else {
            set.insert(a[p], count);
        }
        p = a[p];
    }

    k -= count - dist;
    k %= dist;
    let mut goal: usize = start;
    for _ in 0..k {
        goal = a[goal];
    }
    println!("{}", goal + 1);
}