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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

"use strict";

const main = arg => {
    const input = arg.trim().split("\n");

    const n = BigInt(input[0].split(" ")[0]);
    const k = BigInt(input[0].split(" ")[1]);
    const as = input[1].split(" ").map(n => Number(n));
    as.unshift(0)
    let tmp
    if(n<k){
        let visited = [1]
        let i = 1
        while(!visited.includes(as[i])){
            visited.push(as[i])
            i = as[i]
        }
        let start = visited.indexOf(as[i])
        const len = BigInt(visited.slice(start).length)
        const firstLen = start-1
        tmp = (k-BigInt(start)+1n) % len
        const idx = firstLen + Number(tmp)
        console.log(visited[idx])
    } else {
        tmp = k
        let curr = 1
        while(tmp>0){
            curr = as[curr]
            tmp--
        }
        console.log(curr)
    }
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));  
//1,6,2,5,3,2,5,