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: Accepted)

let () =
  Scanf.scanf "%d %d" @@ fun n k ->
  let a = Array.init (n+1) (fun i -> if i = 0 then 1 else Scanf.scanf " %d" Fun.id) in

  let lv = Array.make (n+1) (-1) in
  let rec loop c i =
    if c = k then i
    else if lv.(i) >= 0 then
      let c' = lv.(i) in
      if (k - c) mod (c - c') = 0 then i
      else loop (c+1) a.(i)
    else begin
      lv.(i) <- c;
      loop (c+1) a.(i)
    end in

  Printf.printf "%d\n" (loop 0 1)