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))
       (m (read))
       (lst (concatenate 'vector (loop :repeat n :collect (1- (read)))))
       (arr (make-array n :initial-element -1 :element-type 'fixnum))
       (st nil)
       (ans 0))
  (setf st (loop :for j :from 0
                 :for k := 0 :then (aref lst k)
                 :if (= -1 (aref arr k)) :do (setf (aref arr k) j)
                   :else :return (list (aref arr k) k)))
  (setf ans (loop :for j :from 1
                  :for k := (aref lst (second st)) :then (aref lst k)
                  :if (= k (second st)) :return j))
  (if (<= (first st) m)
      (loop :for j :from (mod (- m (first st)) ans) :downto 0
            :for k := (second st) :then (aref lst k)
            :finally (princ (1+ k)))
      (loop :for j :from m :downto 0
            :for k := 0 :then (aref lst k)
            :finally (princ (1+ k)))))