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: Runtime Error)

function Main(input) {
  input = input.trim().split("\n").map(function(x) { return x.split(" ")});
  var N = parseInt(input[0][0], 10);
  var K = input[0][1];
  var K1, K2;
  if (K.length > 9){
    K1 = parseInt(K.substr(0, K.length - 9), 10);
    K2 = parseInt(K.substr(-9), 10);

  } else {
    K1 = 0
    K2 = parseInt(K, 10);
  }
  var vec_A = input[1].map(e => (parseInt(e, 10)));
  var mapRecord = Array.from({length: N}, () => 0);
  var tmpTown = 1;
  var loopStart, loopEnd ,loopStartTown, ans;
  for (var i = 0; i <= N; i++){
    mapRecord[tmpTown - 1] ++;
    if (mapRecord[tmpTown - 1] > 1){
      loopEnd = i;
      loopStartTown = tmpTown;
      break;
    }
    tmpTown = vec_A[tmpTown - 1];
  }
  tmpTown = 1;
  for (var i = 0; i <= N; i++){
    if (tmpTown === loopStartTown){
      loopStart = i;
      break;
    }
    tmpTown = vec_A[tmpTown - 1];
  }
  if (K2 > loopStart || K1 > 0){
    K2 = (K2 - loopStart) % (loopEnd - loopStart) + (K1 % (loopEnd - loopStart)) * (1e+9 % (loopEnd - loopStart));
	K2 %= (loopEnd - loopStart);
    tmpTown = loopStartTown;
  } else {
    tmpTown = 1;
  }
  for (var i = 0; i <= N; i++){
    if (i === K2){
      ans = tmpTown;
      break;
    }
    tmpTown = vec_A[tmpTown - 1];
  } 
  console.log(ans);