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: Accepted)

function main(input) {
  const lines = input.trim().split("\n");
  let [n, k] = lines[0].split(' ');
  n = +n;
  k = BigInt(k);
  const towns = lines[1].split(' ').map(Number);

  const visited = new Map();
  let pos = 1, i;
  while (i = visited.get(pos), i === undefined && k) {
    visited.set(pos, visited.size);
    pos = towns[pos - 1];
    k--;
  }
  if (k > 0) {
    const cycle = BigInt(visited.size - i);
    const rest = Number( (k % cycle).toString() );
    for (let [key, value] of visited) {
      if (value == i + rest) {
        pos = key;
        break;
      }
    }
  }
  
  console.log(pos);
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));