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: Accepted)

(let* ((n (read))
       (k (read))
       (a (make-array `(,(1+ n))))
       (last-index 0)
       (memo (make-array `(,(1+ n)) :initial-element nil))
       (hist (make-array `(,(1+ n)) :initial-element nil)))
  ;; input
  (loop :for i :from 1 :to n
        :do (setf (aref a i) (read)))
  ;; init
  (setf (aref hist 0) 1)
  (setf (aref memo 1) 0)
  ;; 
  (loop :for m :from 1 :to n
        :for p :from 0
        :for pos := (aref a (aref hist p))
        :until (aref memo pos)
        :do (progn
              (setf (aref memo pos) m)
              (setf (aref hist m) pos)
              (setf last-index m)))
  (let* ((loop-end (aref hist last-index))
         (loop-start (aref a loop-end))
         (loop-end-index (aref memo loop-end))
         (loop-start-index (aref memo loop-start))
         (period (1+ (- loop-end-index loop-start-index))))
    (cond ((<= k loop-start-index)
           (format t "~A~%" (aref hist k)))
          (t
           (format t "~A~%"
                   (aref hist (+ loop-start-index
                                 (mod (- k loop-start-index) period))))))))