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: Time Limit Exceeded)

"use strict";
var input = require("fs").readFileSync("/dev/stdin", "utf8");
var cin = input.trim().split(/ |\n/), cid = 0;

function main() {
    let N = +cin.shift();
    let K = BigInt(cin[0]);
    let A = cin.map(i=>+i);
    let visit = [];
    let p = 1;
    let offset = BigInt(0);
    let interval = BigInt(0);
    for (let i = 0; i < N; i++) {
        visit.push(p);
        let next = A[p];
        let temp = visit.indexOf(next);
        if (temp >= 0) {
            offset = BigInt(temp);
            interval = BigInt(visit.length - temp);
            break;
        }
        p = next;
    }
    //  console.log(visit)
  	// console.log({interval,offset})
    let ans;
    if (K <= offset) {
        ans = visit[K];
    } else {
        ans = visit[offset + (K - offset) % interval];
    }
    console.log(ans);
}
main();