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 vec = read_vec2::<i64>(2);
    let (N, K) = (vec[0][0], vec[0][1]);
    let A = &vec[1];
 
    let mut routes = Vec::with_capacity(A.len());
    routes.push(1);
    let mut index = 0;
    loop {
        let next = A[*routes.last().unwrap() as usize - 1];
        let before = routes.iter().enumerate().find(|it| *it.1 == next);
        if before.is_none() {
            routes.push(next);
            continue;
        }
 
        index = before.unwrap().0;
        break;
    }
 
    println!("{}", routes[(K % (routes.len() - index) as i64) as usize])
}
 
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
 
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .filter_map(|e| e.parse().ok()).collect()
}
 
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}