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)]
#![allow(unused_variables)]

use itertools::Itertools;
use proconio::{fastout, input};
use std::collections::HashMap;

#[fastout]
fn main() {
    input! {
        n: u64, k: u64,
        a: [usize; n],
    }
    // annotate for rust-analyzer
    let n: u64 = n;
    let k: u64 = k;
    let a: Vec<usize> = a;

    let mut tbl = vec![0; n as usize];

    let mut ans = 0;
    let mut k2 = 0;
    for i in 0..k {
        let idx = a[ans] - 1;
        if tbl[idx] != 0 {
            k2 = tbl[idx] + 1 + ((k - tbl[idx] + 1) % (i - tbl[idx]));
            break;
        } else {
            tbl[idx] = i;
        }
        ans = idx;
    }

    for i in 0..k2 {
        ans = a[ans] - 1;
    }

    println!("{}", ans + 1);
}