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 split_string ?(pattern=" ") = Str.split @@ Str.regexp pattern
let (n, j) = Scanf.sscanf (read_line ())"%d %d" @@ fun n j -> (n, j)
let a = Array.of_list @@ List.map int_of_string @@ split_string @@ read_line ()
let v = Array.make n 0

let rec tp acc i =
  if v.(i) = 1 then (i, List.rev acc)
  else (v.(i) <- 1; tp (i :: acc) (a.(i) - 1))
let tp = tp [] 0

let rec loop (p, acc) i =
  if i = 0 then print_int (List.hd acc + 1)
  else if p = (List.hd acc) then print_int ((List.nth acc (i mod (List.length acc))) + 1)
  else loop (p, (List.tl acc)) (i - 1)

let () = loop tp j