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 proconio::{fastout, input};
use std::collections::BTreeMap;

#[fastout]
fn main() {
    input! {
        n:usize,
        k:usize,
        a:[usize; n]
    }

    let mut cost = BTreeMap::new();
    let mut pos = a[0];
    let mut loop_length = 0;
    let mut loop_start = 0;

    for i in 0..k {
        pos = a[pos - 1];
        match cost.get(&pos) {
            Some(x) => {
                loop_length = i - x;
                loop_start = *x;
                break;
            }
            None => {
                cost.insert(pos, i + 1);
            }
        }
    }

    if loop_length != 0 && loop_start != 0 {
        for _ in 0..(k - loop_start) % loop_length {
            pos = a[pos - 1]
        }
    }

    println!("{}", pos);
}