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)

function main(input) {
  let [n, k] = input[0].trim().split(" ").map(i => BigInt(i));
  let a = input[1].trim().split(" ").map(i => parseInt(i-1));

  let flag = [];
  let sum=0;
  let now=0;
  /* ループの検出 */
  while(true){
    if(flag[a[now]]===undefined){
      flag[a[now]]=sum;
      sum++;
      now=a[now];
    }else{
      break;
    }
  }
  /* ループまでの長さ */
  let firstToLoop = BigInt(flag[a[now]]);
  /* ループの長さ */
  let loop = BigInt(sum-flag[a[now]]);

  /* ループ分をmodしてkを小さくする */
  if((k > firstToLoop)){
    k = (k-firstToLoop)%loop+firstToLoop;
  }

  /* 小さくしたkで再度探索 */
  now=0;
  for(let i=0;i<k;i++){
    now=a[now];
  }

  console.log(now+1);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8').trim().split("\n"));