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\n" @@ fun n k ->
  let tele = Array.make_matrix n 62 0 in
  for i = 0 to n - 1 do
    Scanf.scanf "%d " @@ fun a ->
      tele.(i).(0) <- a - 1
  done;
  for j = 0 to 60 do
    for i = 0 to n - 1 do
      tele.(i).(j + 1) <- tele.(tele.(i).(j)).(j)
    done
  done;
  Printf.printf "%d\n" @@
  succ @@
  List.fold_left (fun c i ->
    if k land (1 lsl i) = 0
    then c
    else tele.(c).(i)) 0 @@
  List.init 62 Fun.id