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)

const main = (input) => {
  input = input.trim().split('\n')

  let [, k] = input[0].split(' ').map(BigInt)
  const cities = input[1].split(' ').map(v => parseInt(v, 10) - 1)

  let loop_size = null
  let before_loop = null

  for (let his=[0], i=0; true;) {
    const head = his.indexOf(cities[i])
    if (head !== -1) {
      before_loop = head
      loop_size = his.length
      break
    }

    his.push(cities[i])
    i = cities[i]
  }

  let start = 0
  let move = k

  if (loop_size < k) {
    start = before_loop
    k -= BigInt(before_loop)
    move = k % BigInt(loop_size)
  }

  let ans = start
  for (let c=0n; c<move; c++) {
    ans = cities[ans]
  }

  return console.log(ans + 1)
}

process.env.MYTEST
  ? (process.env.MYTEST === 'test' ? test() : main(require('fs').readFileSync('dev/stdin', 'utf8')))
  : main(require('fs').readFileSync('/dev/stdin', 'utf8'))