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: Runtime Error)

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 alen = Array.length arr in
  let rec f x i len =
    if x = 1 || i = len then [] else x :: f arr.(x-1) (i+1) len in
  let rec g x k = if k = 0 then x else g arr.(x-1) (k-1) in
  let brr = Array.of_list (f arr.(0) 1 alen) in
  let blen = Array.length brr in
  print_int (if alen <> blen then brr.(k mod blen) else g brr.(blen-1) (k-alen))