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: Runtime Error)

(let* ((n (read))
       (k (read))
       (a (make-array `(,(1+ n))))
       (len 1)
       (mem (make-hash-table :size (ceiling (* n 1.1))))
       (result (make-array `(,n))))
  (loop :for i :from 1 :to n
        :do (setf (aref a i) (read)))
  (setf (aref result 0) 1)
  (setf (gethash 1 mem) 0)
  (block calc
    (loop :for m :from 1 :to k
          :do (let ((next (aref a (aref result (1- m)))))
                (cond ((gethash next mem)
                       (return-from calc))
                      (t
                       (incf len)
                       (setf (gethash next mem) m)
                       (setf (aref result m) next))))))
  (let* ((loop-e (aref result (1- len)))
         (loop-s (aref a loop-e))
         (loop-e-num (1- len))
         (loop-s-num (gethash loop-s mem)))
    (cond ((<= k loop-s-num)
           (format t "~A~%" loop-s))
          (t
           (format t 
                   "~A~%"
                   (aref result 
                         (+ loop-s-num (mod (- k loop-s-num) (1+ (- loop-e-num loop-s-num))))))))))