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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

;;(declaim (optimize (speed 0) (safety 3) (debug 3)))
(declaim (optimize (speed 3) (safety 0) (debug 0)))

(declaim (type fixnum n k))
(defvar n (read))
(defvar k (read))

(defvar *a* (make-array (1+ n) :element-type 'fixnum))
(loop for i from 1 to n do
      (setf (aref *a* i) (read)))

(defvar *prelude*)
(defvar *cycle*)

(let ((v (make-array n :element-type 'fixnum :fill-pointer 0))
      (town 1))
  (loop
   (let ((p (position town v)))
     (when p ; cycle detected
       (setf *prelude* (subseq v 0 p))
       (setf *cycle* (subseq v p))
       (return))
     (vector-push-extend town v)
     (setf town (aref *a* town)))))

(princ (if (< k (length *prelude*))
	   (aref *prelude* k)
	 (aref *cycle* (mod (- k (length *prelude*)) (length *cycle*)))))