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: Wrong Answer)

(defun teleporter (n k)
  (let
   ((a (make-array 0 :fill-pointer 0 :adjustable t))
    (b (make-array 0 :fill-pointer 0 :adjustable t))
    (tmp 1)
    (counter 0))
   (loop :repeat n
         :do (vector-push-extend (read) a))
   (loop :repeat n
         :do (incf counter 1)
             (setq tmp (aref a (- tmp 1)))
             (vector-push-extend tmp b)
         :until (= tmp 1))
   (aref b (mod k counter))))

(print (teleporter (read) (read)))