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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

program main
      implicit none
      integer(16) :: n, k, cnt, roop, i, cnt2, waru
      integer, allocatable :: a(:)
      integer :: str, next, str2, str3
      logical, allocatable :: used(:)

      read *, n, k
      allocate( a(n) )
      read *, a

      allocate( used(n) )
      used = .false.
      cnt = 0
      str = 1
      do
        if ( used(str) ) exit
        used(str) = .true.
        next = a(str)
        str = next
        cnt = cnt + 1
      end do

      str2 = 1
      cnt2 = 1
      do
        next = a(str2)
        str2 = next
        if ( next == str ) exit
        cnt2 = cnt2 + 1
      end do

      if ( (cnt+cnt2) >= k ) then
        str3 = 1
        do i = 1, k
          next = a(str3)
          str3 = next
        end do
        print *, next
      else

        waru = cnt-cnt2
        if ( waru == 0 ) then
          waru = cnt
        end if
  
        roop = mod( k-cnt,waru )
  
        do i = 1, roop
          next = a(str)
          str = next
        end do
        print *, next
      end if

end program main