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 OCaml (4.10.0) (judge verdict: Wrong Answer)

let () =
  let n, k = Scanf.scanf "%d %d\n" @@ fun a b -> a, b in
  let arr = Array.init n @@ fun _ -> Scanf.scanf "%d " @@ fun d -> d in
  let rec f i x = if x = 1 then i else f (i+1) arr.(x-1) in
  let i = f 1 arr.(0) in
  let next = ref arr.(0) in
  for i = 0 to (k mod i) do
    next := arr.(!next - 1)
  done;
  print_int (!next + 1)