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)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{VecDeque, HashMap, BTreeMap, HashSet, BTreeSet};
#[allow(unused_imports)]
use std::io::{stdout, Write, BufWriter};
#[allow(unused_imports)]
use proconio::marker::{Isize1, Usize1, Bytes, Chars};
#[proconio::fastout]
fn main() {
    proconio::input!{
        n: usize,
        k: u128,
        dest: [Usize1; n],
    }
    let mut hist: Vec<usize> = vec![0];
    let mut last = 0usize;
    loop {
        hist.push(dest[last]);
        last = *(hist.last().unwrap());
        if hist[..(hist.len() - 1)].contains(&last) { break; }
    }
    let first = (0usize..).find(|i| hist[*i] == last).unwrap() as u128;
    let last = (hist.len() - 1) as u128;
    if k <= last { println!("{}", hist[k as usize]); }
    else { println!("{}", hist[first as usize + ((k - first) % (last - first)) as usize] + 1); }
}