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 inputs = input.split('\n')
  // console.log(inputs)
  const [N, K] = inputs[0].split(' ').map(BigInt)
  const Ai = inputs[1].split(' ').map(Number)

  // 雑


  // let current = 0
  // const max = 10
  // const path = [1]
  // for(let i = 0; i < K; i++) {
  //   if (max === i) break
  //   current = Ai[current] - 1
  //   path.push(current + 1)
  //   console.log(current)
  // }
  // console.log(path)
  //

  // ループを見つける
  // let loop = [0]
  // let current = 0
  // let count = 0
  // for(let i = 0; i < K; i++) {
  //   console.log(count ++)
  //   current = Ai[current] - 1
  //   if (current === 0) {
  //     console.log('loop found')
  //     break
  //   }
  //   loop.push(current)
  // }
  // console.log(loop)
  // console.log(loop[K % loop.length] + 1)

  // 途中からのループを見つけられない


  let loop = [0]
  let current = 0
  let a = 0
  let visited = []
  for(let i = 0; i < K; i++) {
    current = Ai[current] - 1
    if (visited[current]) {
      // console.log('loop found', current)
      a = loop.indexOf(current)
      loop = loop.slice(loop.indexOf(current))
      break
    }
    visited[current] = true
    loop.push(current)
    // console.log(loop)
  }
  // console.log(a, loop)
  console.log(loop[(K - BigInt(a)) % BigInt(loop.length)] + 1)

}

// main(
//   `6 10
// 6 5 2 5 3 2`
// )
// main(
//   `4 5
// 3 2 4 1`
// )

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