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: Accepted)

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: usize,
        mut k: u64,
        mut a: [usize; n],
    }
    for i in 0..n {
        a[i] = a[i] - 1;
    }

    let mut b = vec![0; n];
    for i in 0..n {
        b[i] = i;
    }
    for i in 0..63 {
        let t = 1 << i;
        if (k & t) != 0 {
            for j in 0..n {
                b[j] = a[b[j]];
            }
        }
        let mut tmp = vec![0; n];
        for j in 0..n {
            tmp[j] = a[a[j]];
        }
        a = tmp;

        // eprintln!("{:?}", a);
    }
    println!("{}", b[0] + 1);
}