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: Runtime Error)

#![allow(unused_imports)]
use itertools::Itertools;
use proconio::{input, marker::*};
use std::cmp::*;
use std::collections::*;
use superslice::*;

fn main() {
    input! {
        n: usize,
        k: usize,
        a: [Usize1;n]
    }

    let mut v: Vec<usize> = Vec::new();
    let mut seen: Vec<bool> = vec![false; n];

    let mut i = 0;

    let mut loop_start = 0;
    let mut loop_end = 0;
    let mut loop_len = 0;

    for _ in 0..n {
        if seen[a[i]] {
            loop_end = v.len() - 1;
            loop_start = a[i];
            loop_len = v.len() - v.iter().position(|&x| x == a[i]).unwrap();
            break;
        }
        seen[a[i]] = true;
        v.push(a[i]);
        i = a[i];
    }

    let bef_loop = v.len() - loop_len;

    dbg!(&v, &seen);
    dbg!(bef_loop, loop_start, loop_end, loop_len);
    if k - 1 <= v.len() {
        println!("{}", v.get(k - 1).unwrap() + 1);
    } else {
        let k = k - bef_loop - 1;
        let ans = v.get(bef_loop + k % loop_len).unwrap() + 1;
        println!("{}", ans);
    }
}